Show commands:
SageMath
E = EllipticCurve("bv1")
E.isogeny_class()
Elliptic curves in class 122694.bv
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
122694.bv1 | 122694cq4 | \([1, 1, 1, -7198474, 7430764661]\) | \(4824238966273/66\) | \(564365114204034\) | \([2]\) | \(3686400\) | \(2.3865\) | |
122694.bv2 | 122694cq2 | \([1, 1, 1, -450304, 115748381]\) | \(1180932193/4356\) | \(37248097537466244\) | \([2, 2]\) | \(1843200\) | \(2.0399\) | |
122694.bv3 | 122694cq3 | \([1, 1, 1, -245814, 221592405]\) | \(-192100033/2371842\) | \(-20281589109150369858\) | \([2]\) | \(3686400\) | \(2.3865\) | |
122694.bv4 | 122694cq1 | \([1, 1, 1, -41324, -74755]\) | \(912673/528\) | \(4514920913632272\) | \([2]\) | \(921600\) | \(1.6933\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 122694.bv have rank \(1\).
Complex multiplication
The elliptic curves in class 122694.bv do not have complex multiplication.Modular form 122694.2.a.bv
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.