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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 2320.c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2320.c1 | 2320g1 | \([0, 0, 0, -8, 7]\) | \(3538944/725\) | \(11600\) | \([2]\) | \(96\) | \(-0.50465\) | \(\Gamma_0(N)\)-optimal |
| 2320.c2 | 2320g2 | \([0, 0, 0, 17, 42]\) | \(2122416/4205\) | \(-1076480\) | \([2]\) | \(192\) | \(-0.15807\) |
Rank
sage: E.rank()
The elliptic curves in class 2320.c have rank \(1\).
Complex multiplication
The elliptic curves in class 2320.c do not have complex multiplication.Modular form 2320.2.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.
