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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 7616.c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 7616.c1 | 7616b2 | \([0, 1, 0, -1793, 2911]\) | \(2433138625/1387778\) | \(363797676032\) | \([2]\) | \(6144\) | \(0.90812\) | |
| 7616.c2 | 7616b1 | \([0, 1, 0, -1153, -15393]\) | \(647214625/3332\) | \(873463808\) | \([2]\) | \(3072\) | \(0.56154\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 7616.c have rank \(1\).
Complex multiplication
The elliptic curves in class 7616.c do not have complex multiplication.Modular form 7616.2.a.c
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
