gh-37609: src/sage/schemes: Doctest cosmetics
    
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Standard reformatting of doctests and their outputs

Split out from #35095


### 📝 Checklist

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- [ ] The title is concise and informative.
- [ ] The description explains in detail what this PR is about.
- [ ] I have linked a relevant issue or discussion.
- [ ] I have created tests covering the changes.
- [ ] I have updated the documentation accordingly.

### ⌛ Dependencies

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URL: #37609
Reported by: Matthias Köppe
Reviewer(s): Giacomo Pope, Matthias Köppe

Author: Release Manager

src/sage/schemes/elliptic_curves/Qcurves.py

@@ -195,11 +195,11 @@ def is_Q_curve(E, maxp=100, certificate=False, verbose=False):
         True
         sage: cert
         {'CM': 0,
-        'N': 2,
-        'core_degs': [1, 2],
-        'core_poly': x^2 - 840064*x + 1593413632,
-        'r': 1,
-        'rho': 1}
+         'N': 2,
+         'core_degs': [1, 2],
+         'core_poly': x^2 - 840064*x + 1593413632,
+         'r': 1,
+         'rho': 1}
 
     TESTS::
 

src/sage/schemes/elliptic_curves/ell_curve_isogeny.py

@@ -1229,7 +1229,8 @@ def _call_(self, P):
             Traceback (most recent call last):
             ...
             TypeError: (20 : 90 : 1) fails to convert into the map's domain
-            Elliptic Curve defined by y^2 = x^3 + 7*x over Number Field in th with defining polynomial x^2 + 3,
+            Elliptic Curve defined by y^2 = x^3 + 7*x over
+            Number Field in th with defining polynomial x^2 + 3,
             but a `pushforward` method is not properly implemented
 
         Check that copying the order over works::

src/sage/schemes/elliptic_curves/ell_generic.py

@@ -546,11 +546,11 @@ def __call__(self, *args, **kwds):
             sage: T = E.torsion_subgroup()
             sage: [E(t) for t in T]
             [(0 : 1 : 0),
-            (9 : 23 : 1),
-            (2 : 2 : 1),
-            (1 : -1 : 1),
-            (2 : -5 : 1),
-            (9 : -33 : 1)]
+             (9 : 23 : 1),
+             (2 : 2 : 1),
+             (1 : -1 : 1),
+             (2 : -5 : 1),
+             (9 : -33 : 1)]
 
         ::
 

src/sage/schemes/elliptic_curves/ell_local_data.py

@@ -742,7 +742,7 @@ def _tate(self, proof=None, globally=False):
             sage: # needs sage.rings.number_field
             sage: K.<t> = NumberField(x^7 - 2*x + 177)
             sage: E = EllipticCurve([0,1,0,t,t])
-            sage: P = K.ideal(2,t^3 + t + 1)
+            sage: P = K.ideal(2, t^3 + t + 1)
             sage: E.local_data(P).kodaira_symbol()
             II
         """
@@ -1142,29 +1142,29 @@ def check_prime(K, P):
 
     .. NOTE::
 
-        If `P` is not a prime and does not generate a prime, a ``TypeError``
+        If `P` is not a prime and does not generate a prime, a :class:`TypeError`
         is raised.
 
     EXAMPLES::
 
         sage: from sage.schemes.elliptic_curves.ell_local_data import check_prime
-        sage: check_prime(QQ,3)
+        sage: check_prime(QQ, 3)
         3
-        sage: check_prime(QQ,QQ(3))
+        sage: check_prime(QQ, QQ(3))
         3
-        sage: check_prime(QQ,ZZ.ideal(31))
+        sage: check_prime(QQ, ZZ.ideal(31))
         31
 
         sage: # needs sage.rings.number_field
         sage: x = polygen(ZZ, 'x')
         sage: K.<a> = NumberField(x^2 - 5)
         sage: check_prime(K, a)
         Fractional ideal (a)
-        sage: check_prime(K,a+1)
+        sage: check_prime(K, a + 1)
         Fractional ideal (a + 1)
-        sage: [check_prime(K,P) for P in K.primes_above(31)]
+        sage: [check_prime(K, P) for P in K.primes_above(31)]
         [Fractional ideal (5/2*a + 1/2), Fractional ideal (5/2*a - 1/2)]
-        sage: L.<b> = NumberField(x^2+3)
+        sage: L.<b> = NumberField(x^2 + 3)
         sage: check_prime(K, L.ideal(5))
         Traceback (most recent call last):
         ...

src/sage/schemes/elliptic_curves/ell_point.py

@@ -3265,23 +3265,23 @@ def archimedean_local_height(self, v=None, prec=None, weighted=False):
     def non_archimedean_local_height(self, v=None, prec=None,
                                      weighted=False, is_minimal=None):
         """
-        Compute the local height of self at the non-archimedean place `v`.
+        Compute the local height of ``self`` at the non-archimedean place `v`.
 
         INPUT:
 
         - ``self`` -- a point on an elliptic curve over a number field
           `K`.
 
-        - ``v`` -- a non-archimedean place of `K`, or None (default).
+        - ``v`` -- a non-archimedean place of `K`, or ``None`` (default).
           If `v` is a non-archimedean place, return the local height
-          of self at `v`. If `v` is None, return the total
+          of self at `v`. If `v` is ``None``, return the total
           non-archimedean contribution to the global height.
 
-        - ``prec`` -- integer, or None (default). The precision of the
-          computation. If None, the height is returned symbolically.
+        - ``prec`` -- integer, or ``None`` (default). The precision of the
+          computation. If ``None``, the height is returned symbolically.
 
-        - ``weighted`` -- boolean. If False (default), the height is
-          normalised to be invariant under extension of `K`. If True,
+        - ``weighted`` -- boolean. If ``False`` (default), the height is
+          normalised to be invariant under extension of `K`. If ``True``,
           return this normalised height multiplied by the local degree
           if `v` is a single place, or by the degree of `K` if `v` is
           None.

src/sage/schemes/elliptic_curves/gal_reps_number_field.py

@@ -80,7 +80,9 @@ class GaloisRepresentation(SageObject):
         sage: E = EllipticCurve('11a1').change_ring(K)
         sage: rho = E.galois_representation()
         sage: rho
-        Compatible family of Galois representations associated to the Elliptic Curve defined by y^2 + y = x^3 + (-1)*x^2 + (-10)*x + (-20) over Number Field in a with defining polynomial x^2 + 1
+        Compatible family of Galois representations associated to the Elliptic Curve
+         defined by y^2 + y = x^3 + (-1)*x^2 + (-10)*x + (-20)
+         over Number Field in a with defining polynomial x^2 + 1
     """
 
     def __init__(self, E):
@@ -94,7 +96,9 @@ def __init__(self, E):
             sage: E = EllipticCurve('11a1').change_ring(K)
             sage: rho = E.galois_representation()
             sage: rho
-            Compatible family of Galois representations associated to the Elliptic Curve defined by y^2 + y = x^3 + (-1)*x^2 + (-10)*x + (-20) over Number Field in a with defining polynomial x^2 + 1
+            Compatible family of Galois representations associated to the Elliptic Curve
+             defined by y^2 + y = x^3 + (-1)*x^2 + (-10)*x + (-20)
+             over Number Field in a with defining polynomial x^2 + 1
             sage: loads(rho.dumps()) == rho
             True
         """
@@ -111,12 +115,16 @@ def __repr__(self):
             sage: E = EllipticCurve('11a1').change_ring(K)
             sage: rho = E.galois_representation()
             sage: rho
-            Compatible family of Galois representations associated to the Elliptic Curve defined by y^2 + y = x^3 + (-1)*x^2 + (-10)*x + (-20) over Number Field in a with defining polynomial x^2 + 1
+            Compatible family of Galois representations associated to the Elliptic Curve
+             defined by y^2 + y = x^3 + (-1)*x^2 + (-10)*x + (-20)
+             over Number Field in a with defining polynomial x^2 + 1
 
             sage: K.<a> = NumberField(x^2-x+1)
             sage: E = EllipticCurve([0,0,0,a,0])
             sage: E.galois_representation()
-            Compatible family of Galois representations associated to the CM Elliptic Curve defined by y^2 = x^3 + a*x over Number Field in a with defining polynomial x^2 - x + 1
+            Compatible family of Galois representations associated to the
+             CM Elliptic Curve defined by y^2 = x^3 + a*x
+             over Number Field in a with defining polynomial x^2 - x + 1
         """
         if self.E.has_cm():
             return "Compatible family of Galois representations associated to the CM " + repr(self.E)
@@ -225,10 +233,10 @@ def is_surjective(self, p, A=100):
 
         INPUT:
 
-        * ``p`` - int - a prime number.
+        * ``p`` -- a prime number.
 
-        * ``A`` - int - a bound on the number of traces of Frobenius to use
-                     while trying to prove surjectivity.
+        * ``A`` -- (integer) a bound on the number of traces of Frobenius to use
+          while trying to prove surjectivity.
 
         EXAMPLES::
 
@@ -258,7 +266,7 @@ def is_surjective(self, p, A=100):
 
         For CM curves, the mod-p representation is never surjective::
 
-            sage: K.<a> = NumberField(x^2-x+1)
+            sage: K.<a> = NumberField(x^2 - x + 1)
             sage: E = EllipticCurve([0,0,0,0,a])
             sage: E.has_cm()
             True
@@ -320,7 +328,7 @@ def isogeny_bound(self, A=100):
         `p` for which the mod-`p` representation is reducible, and [0]
         is returned::
 
-            sage: K.<a> = NumberField(x^2-x+1)
+            sage: K.<a> = NumberField(x^2 - x + 1)
             sage: E = EllipticCurve([0,0,0,0,a])
             sage: E.has_rational_cm()
             True
@@ -403,7 +411,7 @@ def reducible_primes(self):
         `p` for which the mod-`p` representation is reducible, and [0]
         is returned::
 
-            sage: K.<a> = NumberField(x^2-x+1)
+            sage: K.<a> = NumberField(x^2 - x + 1)
             sage: E = EllipticCurve([0,0,0,0,a])
             sage: E.has_rational_cm()
             True
@@ -426,7 +434,7 @@ def _non_surjective(E, patience=100):
     - ``E`` -- EllipticCurve (over a number field).
 
     - ``A`` -- int (a bound on the number of traces of Frobenius to use
-                 while trying to prove surjectivity).
+      while trying to prove surjectivity).
 
     OUTPUT:
 
@@ -848,7 +856,8 @@ def _semistable_reducible_primes(E, verbose=False):
 
         sage: x = polygen(ZZ, 'x')
         sage: K.<a> = NumberField(x^5 - 6*x^3 + 8*x - 1)
-        sage: E = EllipticCurve(K, [a^3 - 2*a, a^4 - 2*a^3 - 4*a^2 + 6*a + 1, a + 1, -a^3 + a + 1, -a])
+        sage: E = EllipticCurve(K, [a^3 - 2*a, a^4 - 2*a^3 - 4*a^2 + 6*a + 1,
+        ....:                       a + 1, -a^3 + a + 1, -a])
         sage: from sage.schemes.elliptic_curves.gal_reps_number_field import _semistable_reducible_primes
         sage: _semistable_reducible_primes(E)
         [2, 5, 53, 1117]
@@ -1406,7 +1415,7 @@ def Billerey_R_bound(E, max_l=200, num_l=8, small_prime_bound=None, debug=False)
 
     .. NOTE::
 
-        The purpose of the small_prime_bound is that it is faster to
+        The purpose of the ``small_prime_bound`` is that it is faster to
         deal with these using the local test; by ignoring them here,
         we enable the algorithm to terminate sooner when there are no
         large reducible primes, which is always the case in practice.