diff --git a/lmfdb/abvar/fq/isog_class.py b/lmfdb/abvar/fq/isog_class.py
index 4a93cbca8f..361e28e4d0 100644
--- a/lmfdb/abvar/fq/isog_class.py
+++ b/lmfdb/abvar/fq/isog_class.py
@@ -84,6 +84,11 @@ def __init__(self, dbdata):
             dbdata["hyp_count"] = None
         if "jacobian_count" not in dbdata:
             dbdata["jacobian_count"] = None
+        # New invariants: cyclicity and noncyclic primes
+        if "is_cyclic" not in dbdata:
+            dbdata["is_cyclic"] = None       
+        if "noncyclic_primes" not in dbdata:
+            dbdata["noncyclic_primes"] = []
         self.__dict__.update(dbdata)
 
     @classmethod
@@ -232,9 +237,15 @@ def properties(self):
             ("Primitive", "yes" if self.is_primitive else "no"),
         ]
         if self.has_principal_polarization != 0:
-            props += [("Principally polarizable", "yes" if self.has_principal_polarization == 1 else "no")]
+            props += [(
+                "Principally polarizable",
+                "yes" if self.has_principal_polarization == 1 else "no",
+            )]
         if self.has_jacobian != 0:
-            props += [("Contains a Jacobian", "yes" if self.has_jacobian == 1 else "no")]
+            props += [(
+                "Contains a Jacobian",
+                "yes" if self.has_jacobian == 1 else "no",
+            )]
         return props
 
     # at some point we were going to display the weil_numbers instead of the frobenius angles
diff --git a/lmfdb/abvar/fq/main.py b/lmfdb/abvar/fq/main.py
index 52c81732ec..8cf5ac3024 100644
--- a/lmfdb/abvar/fq/main.py
+++ b/lmfdb/abvar/fq/main.py
@@ -23,6 +23,7 @@
 from lmfdb.utils import redirect_no_cache
 from lmfdb.utils.search_columns import SearchColumns, SearchCol, MathCol, LinkCol, ProcessedCol, CheckCol, CheckMaybeCol
 from lmfdb.abvar.fq.download import AbvarFq_download
+from lmfdb.utils.search_parsing import parse_primes
 
 logger = make_logger("abvarfq")
 
@@ -399,8 +400,31 @@ def nbsp(knowl, label):
         jacobian = YesNoMaybeBox(
             "jacobian",
             label="Jacobian",
-            knowl="ag.jacobian"
+            knowl="ag.jacobian",
         )
+
+        # Cyclic group of points (advanced yes/no box)
+        cyclic = YesNoBox(
+            "cyclic",
+            label="Cyclic group of points",
+            knowl="av.fq.cyclic_group_points",
+            advanced=True,
+        )
+
+        # Non-cyclic primes with mode selector (include / exactly / subset)
+        noncyclic_mode = SubsetBox(
+            "noncyclic_primes_mode",
+            advanced=True,
+        )
+        noncyclic_primes = TextBoxWithSelect(
+            "noncyclic_primes",
+            label="Non-cyclic primes",
+            select_box=noncyclic_mode,
+            knowl="av.fq.noncyclic_primes",
+            example="2 or 2,3,5",
+            advanced=True,
+        )
+
         uglabel = "Use %s in the following inputs" % display_knowl("av.decomposition", "Geometric decomposition")
         use_geom_decomp = CheckBox(
             "use_geom_decomp",
@@ -506,6 +530,7 @@ def short_label(d):
             [newton_polygon, abvar_point_count, curve_point_count, simple_factors],
             [newton_elevation, jac_cnt, hyp_cnt, twist_count, max_twist_degree],
             [angle_rank, angle_corank, geom_deg, p_corank, geom_squarefree],
+            [cyclic, noncyclic_primes],
             use_geom_refine,
             [dim1, dim2, dim3, dim4, dim5],
             [dim1d, dim2d, dim3d, number_field, galois_group],
@@ -516,6 +541,7 @@ def short_label(d):
             [g, geom_simple],
             [initial_coefficients, polarizable],
             [p_rank, jacobian],
+            [cyclic, noncyclic_primes],
             [p_corank, geom_squarefree],
             [jac_cnt, hyp_cnt],
             [angle_rank, angle_corank],
@@ -536,6 +562,7 @@ def short_label(d):
             [count],
         ]
 
+
     def search_types(self, info):
         return self._search_again(info, [
             ('List', 'List of isogeny classes'),
@@ -552,6 +579,7 @@ def common_parse(info, query):
     parse_bool(info, query, "primitive", qfield="is_primitive")
     parse_bool_unknown(info, query, "jacobian", qfield="has_jacobian")
     parse_bool_unknown(info, query, "polarizable", qfield="has_principal_polarization")
+    parse_bool(info, query, "cyclic", qfield="is_cyclic")
     parse_ints(info, query, "p_rank")
     parse_ints(info, query, "p_corank", qfield="p_rank_deficit")
     parse_ints(info, query, "angle_rank")
@@ -561,6 +589,14 @@ def common_parse(info, query):
     parse_ints(info, query, "hyp_cnt", qfield="hyp_count", name="Number of Hyperelliptic Jacobians")
     parse_ints(info, query, "twist_count")
     parse_ints(info, query, "max_twist_degree")
+    parse_primes(
+        info,
+        query,
+        "noncyclic_primes",
+        qfield="noncyclic_primes",
+        mode=info.get("noncyclic_primes_mode"),
+    )
+
     parse_ints(info, query, "size")
     parse_newton_polygon(info, query, "newton_polygon", qfield="slopes")
     parse_string_start(info, query, "initial_coefficients", qfield="poly_str", initial_segment=["1"])
@@ -680,7 +716,7 @@ def extended_code(c):
     ProcessedCol("number_fields", "av.fq.number_field", "Number fields", lambda nfs: ", ".join(nf_display_knowl(nf, field_pretty(nf)) for nf in nfs), default=False),
     SearchCol("galois_groups_pretty", "nf.galois_group", "Galois groups", download_col="galois_groups", default=False),
     SearchCol("decomposition_display_search", "av.decomposition", "Isogeny factors", download_col="decompositionraw")],
-    db_cols=["label", "g", "q", "poly", "p_rank", "p_rank_deficit", "is_simple", "is_geometrically_simple", "simple_distinct", "simple_multiplicities", "is_primitive", "primitive_models", "curve_count", "curve_counts", "abvar_count", "abvar_counts", "jacobian_count", "hyp_count", "number_fields", "galois_groups", "slopes", "newton_elevation", "twist_count", "max_twist_degree", "geometric_extension_degree", "angle_rank", "angle_corank", "is_supersingular", "has_principal_polarization", "has_jacobian"])
+    db_cols=["label", "g", "q", "poly", "p_rank", "p_rank_deficit", "is_simple", "is_geometrically_simple", "simple_distinct", "simple_multiplicities", "is_primitive", "primitive_models", "curve_count", "curve_counts", "abvar_count", "abvar_counts", "jacobian_count", "hyp_count", "number_fields", "galois_groups", "slopes", "newton_elevation", "twist_count", "max_twist_degree", "geometric_extension_degree", "angle_rank", "angle_corank", "is_supersingular", "has_principal_polarization", "has_jacobian", "is_cyclic", "noncyclic_primes"])
 
 def abvar_postprocess(res, info, query):
     gals = set()
diff --git a/lmfdb/abvar/fq/templates/show-abvarfq.html b/lmfdb/abvar/fq/templates/show-abvarfq.html
index bc8290a69f..ae6986b148 100644
--- a/lmfdb/abvar/fq/templates/show-abvarfq.html
+++ b/lmfdb/abvar/fq/templates/show-abvarfq.html
@@ -31,6 +31,27 @@ <h2>Invariants</h2>
     {% if cl.size is not none %}
     <tr><td>{{KNOWL('av.fq.isogeny_class_size',title='Isomorphism classes')}}:</td><td>&nbsp;&nbsp;{{cl.size}}</td></tr>
     {% endif %}
+    {# --- NEW: cyclicity invariants --- #}
+    {% if cl.is_cyclic is not none %}
+      <tr>
+        <td>{{ KNOWL('av.fq.cyclic_group_points', title='Cyclic group of points') }}:</td>
+        <td>&nbsp;&nbsp;
+          {% if cl.is_cyclic %}
+            yes
+          {% else %}
+            no
+          {% endif %}
+        </td>
+      </tr>
+    {% endif %}
+
+
+    {% if cl.noncyclic_primes %}
+    <tr>
+      <td>{{ KNOWL('av.fq.noncyclic_primes', title='Non-cyclic primes') }}:</td>
+      <td>&nbsp;&nbsp;${{ cl.noncyclic_primes|join(', ') }}$</td>
+    </tr>
+    {% endif %}
 </table>
 </p>
 
diff --git a/lmfdb/abvar/fq/test_av.py b/lmfdb/abvar/fq/test_av.py
index e7c4cf0ca6..95dd68cec2 100644
--- a/lmfdb/abvar/fq/test_av.py
+++ b/lmfdb/abvar/fq/test_av.py
@@ -157,3 +157,12 @@ def test_download_curves(self):
 
         page = self.tc.get('Variety/Abelian/Fq/download_curves/5.3.ac_e_ai_v_abl', follow_redirects=True)
         assert 'No curves for abelian variety isogeny class 5.3.ac_e_ai_v_abl' in page.get_data(as_text=True)
+
+    def test_cyclic_group_of_points_display(self):
+        r"""
+        Check that the cyclic group of points information is displayed
+        on the isogeny-class page.
+        """
+        page = self.tc.get("/Variety/Abelian/Fq/2/9/aj_bl").get_data(as_text=True)
+        assert "Cyclic" in page
+
diff --git a/lmfdb/abvar/fq/test_browse_page.py b/lmfdb/abvar/fq/test_browse_page.py
index 55ac1771f7..07785af791 100644
--- a/lmfdb/abvar/fq/test_browse_page.py
+++ b/lmfdb/abvar/fq/test_browse_page.py
@@ -12,9 +12,10 @@ def test_index_page(self):
         """
         homepage = self.tc.get("/Variety/Abelian/Fq/").get_data(as_text=True)
         assert "by dimension and base field" in homepage
+        assert "Cyclic group of points" in homepage
 
     def test_stats_page(self):
-        self.check_args("/Variety/Abelian/Fq/stats","Abelian variety isogeny classes: Statistics")
+        self.check_args("/Variety/Abelian/Fq/stats", "Abelian variety isogeny classes: Statistics")
 
     # TODO test dynamic stats
 
@@ -43,7 +44,10 @@ def test_lookup(self):
         r"""
         Check that Variety/Abelian/Fq/?jump works
         """
-        self.check_args("/Variety/Abelian/Fq/?jump=x^6-3*x^5%2B3*x^4-2*x^3%2B6*x^2-12*x%2B8", "3.2.ad_d_ac")
+        self.check_args(
+            "/Variety/Abelian/Fq/?jump=x^6-3*x^5%2B3*x^4-2*x^3%2B6*x^2-12*x%2B8",
+            "3.2.ad_d_ac"
+        )
 
     # Various searches
     # Many things are checked twice: Once from main index/browse page, and once from the refining search page
@@ -148,7 +152,10 @@ def test_search_newton(self):
         # slope not a rational number
         self.check_args("/Variety/Abelian/Fq/?newton_polygon=t", "is not a valid input")
         # slopes are not increasing
-        self.check_args("/Variety/Abelian/Fq/?start=&count=&newton_polygon=%5B1%2C1%2F2%2C0%5D", "Slopes must be increasing")
+        self.check_args(
+            "/Variety/Abelian/Fq/?start=&count=&newton_polygon=%5B1%2C1%2F2%2C0%5D",
+            "Slopes must be increasing"
+        )
 
     def test_search_initcoeffs(self):
         r"""
@@ -157,7 +164,10 @@ def test_search_initcoeffs(self):
         self.check_args("/Variety/Abelian/Fq/?initial_coefficients=%5B1%2C-1%2C3%2C9%5D", "4.3.b_ab_d_j")
         self.check_args("/Variety/Abelian/Fq/?initial_coefficients=%5B1%2C-1%2C3%2C9%5D", "4.3.b_ab_d_j")
         # there should be only one match, if ranges were supported
-        self.check_args("/Variety/Abelian/Fq/?angle_ranks=&initial_coefficients=%5B3%2C+9%2C+10%2C+87-100%5D", "Ranges not supported")
+        self.check_args(
+            "/Variety/Abelian/Fq/?angle_ranks=&initial_coefficients=%5B3%2C+9%2C+10%2C+87-100%5D",
+            "Ranges not supported"
+        )
 
     def test_search_pointcountsav(self):
         r"""
@@ -187,8 +197,14 @@ def test_search_isogfactor(self):
         Check that we can search by decomposition into isogeny factors
         """
         # [3.5.ah_y_ach,*]
-        self.check_args("/Variety/Abelian/Fq/?simple_quantifier=include&simple_factors=3.5.ah_y_ach", "4.5.ak_by_agk_qb")
-        self.check_args("/Variety/Abelian/Fq/?p_rank=4&dim1_factors=2&dim2_factors=2&dim1_distinct=1&dim2_distinct=1", "6.2.ag_p_aw_bh_acu_ey")
+        self.check_args(
+            "/Variety/Abelian/Fq/?simple_quantifier=include&simple_factors=3.5.ah_y_ach",
+            "4.5.ak_by_agk_qb"
+        )
+        self.check_args(
+            "/Variety/Abelian/Fq/?p_rank=4&dim1_factors=2&dim2_factors=2&dim1_distinct=1&dim2_distinct=1",
+            "6.2.ag_p_aw_bh_acu_ey"
+        )
         self.check_args("/Variety/Abelian/Fq/?dim1_factors=6&dim1_distinct=1", "5 matches")
 
     def test_search_numberfield(self):
@@ -274,8 +290,54 @@ def test_search_combos(self):
         self.check_args("/Variety/Abelian/Fq/?p_rank=2&initial_coefficients=%5B1%2C-1%2C3%2C9%5D", "4.3.b_ab_d_j")
         self.check_args("/Variety/Abelian/Fq/?p_rank=2&initial_coefficients=%5B1%2C-1%2C3%2C9%5D", "4.3.b_ab_d_j")
         # initial coefficients and point counts of the abelian variety
-        self.check_args("/Variety/Abelian/Fq/?initial_coefficients=%5B1%2C-1%2C3%2C9%5D&abvar_point_count=%5B75%2C7125%5D", "No matches")
-        self.check_args("/Variety/Abelian/Fq/?initial_coefficients=%5B1%2C-1%2C3%2C9%5D&abvar_point_count=%5B75%2C7125%5D", "No matches")
+        self.check_args(
+            "/Variety/Abelian/Fq/?initial_coefficients=%5B1%2C-1%2C3%2C9%5D&abvar_point_count=%5B75%2C7125%5D",
+            "No matches"
+        )
+        self.check_args(
+            "/Variety/Abelian/Fq/?initial_coefficients=%5B1%2C-1%2C3%2C9%5D&abvar_point_count=%5B75%2C7125%5D",
+            "No matches"
+        )
         # Combining unknown fields on Jacobian and Principal polarization.
         self.check_args("/Variety/Abelian/Fq/?g=3&jacobian=no&polarizable=not_no", "3.2.a_a_ae")
         self.check_args("/Variety/Abelian/Fq/?g=3&jacobian=no&polarizable=yes", "3.2.a_ac_a")
+
+    def test_search_cyclic_group(self):
+        r"""
+        Check that we can restrict to cyclic or non-cyclic groups of points
+        using the cyclic search parameter.
+        """
+        # 1.2.ac has cyclic group of points (is_cyclic = True)
+        self.check_args(
+            "/Variety/Abelian/Fq/?cyclic=yes",
+            ">1.2.ac<",
+        )
+
+        # 1.3.a has non-cyclic group of points (is_cyclic = False)
+        self.check_args(
+            "/Variety/Abelian/Fq/?cyclic=no",
+            ">1.3.a<",
+        )
+
+        # And make sure they do not appear in the wrong list
+        self.not_check_args(
+            "/Variety/Abelian/Fq/?cyclic=yes",
+            ">1.3.a<",
+        )
+        self.not_check_args(
+            "/Variety/Abelian/Fq/?cyclic=no",
+            ">1.2.ac<",
+        )
+
+    def test_search_noncyclic_primes(self):
+        r"""
+        Check that the noncyclic_primes search parameter is accepted and
+        finds classes that are non-cyclic at p = 2.
+        """
+        self.check_args(
+            "/Variety/Abelian/Fq/?noncyclic_primes=2",
+            ">1.3.a<",
+        )
+
+
+