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Author: user202729

src/sage/libs/eclib/interface.py

@@ -272,7 +272,7 @@ def two_descent(self, verbose=True, selmer_only=False, first_limit=20,
           testing local solubility; very simple search with no
           overheads).
 
-        - ``second_limit`` -- integer (default: 8); naive height bound on
+        - ``second_limit`` -- integer (default: 8); logarithmic height bound on
           second point search on quartic homogeneous spaces (after
           testing local solubility; sieve-assisted search)
 

src/sage/schemes/elliptic_curves/ell_rational_field.py

@@ -808,8 +808,28 @@ def two_descent(self, verbose=True,
 
         - ``selmer_only`` -- boolean (default: ``False``); selmer_only switch
 
-        - ``first_limit``, ``second_limit``, ``n_aux``, ``second_descent`` --
-          see :meth:`~sage.libs.eclib.interface.mwrank_EllipticCurve.two_descent`
+        - ``first_limit`` -- integer (default: 20); naive height bound on
+          first point search on quartic homogeneous spaces (before
+          testing local solubility; very simple search with no
+          overheads).
+
+        - ``second_limit`` -- integer (default: 8); logarithmic height bound on
+          second point search on quartic homogeneous spaces (after
+          testing local solubility; sieve-assisted search)
+
+        - ``n_aux`` -- integer (default: -1); if positive, the number of
+          auxiliary primes used in sieve-assisted search for quartics.
+          If -1 (the default) use a default value (set in the eclib
+          code in ``src/qrank/mrank1.cc`` in DEFAULT_NAUX: currently 8).
+          Only relevant for curves with no 2-torsion, where full
+          2-descent is carried out.  Worth increasing for curves
+          expected to be of rank > 6 to one or two more than the
+          expected rank.
+
+        - ``second_descent`` -- boolean (default: ``True``); flag specifying
+          whether or not a second descent will be carried out.  Only relevant
+          for curves with 2-torsion.  Recommended left as the default except for
+          experts interested in details of Selmer groups.
 
         OUTPUT:
 
@@ -2260,7 +2280,10 @@ def gens(self, proof=None, **kwds):
         - ``use_database`` -- boolean (default: ``True``); if ``True``, attempts to
           find curve and gens in the (optional) database
 
-        - ``descent_second_limit`` -- (default: 12) used in 2-descent.  See ``second_limit``
+        - ``descent_second_limit`` -- (default: 12); logarithmic height bound on
+          second point search on quartic homogeneous spaces (after
+          testing local solubility; sieve-assisted search). Used in 2-descent.
+          See also ``second_limit``
           in :meth:`~sage.libs.eclib.interface.mwrank_EllipticCurve.two_descent`
 
         - ``sat_bound`` -- (default: 1000) bound on primes used in