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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 1288.c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1288.c1 | 1288f2 | \([0, 1, 0, -16968, 118384]\) | \(263822189935250/149429406721\) | \(306031424964608\) | \([2]\) | \(3840\) | \(1.4695\) | |
| 1288.c2 | 1288f1 | \([0, 1, 0, 4192, 16816]\) | \(7953970437500/4703287687\) | \(-4816166591488\) | \([2]\) | \(1920\) | \(1.1229\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1288.c have rank \(1\).
Complex multiplication
The elliptic curves in class 1288.c do not have complex multiplication.Modular form 1288.2.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.
