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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 880.c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 880.c1 | 880e1 | \([0, -1, 0, -1416, -20240]\) | \(-76711450249/851840\) | \(-3489136640\) | \([]\) | \(672\) | \(0.64596\) | \(\Gamma_0(N)\)-optimal |
| 880.c2 | 880e2 | \([0, -1, 0, 4744, -108944]\) | \(2882081488391/2883584000\) | \(-11811160064000\) | \([]\) | \(2016\) | \(1.1953\) |
Rank
sage: E.rank()
The elliptic curves in class 880.c have rank \(0\).
Complex multiplication
The elliptic curves in class 880.c do not have complex multiplication.Modular form 880.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
