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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 1288c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1288.b1 | 1288c1 | \([0, 0, 0, 24425, -37215701]\) | \(100718081964000000/37453512751940327\) | \(-599256204031045232\) | \([]\) | \(24480\) | \(2.0903\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 1288c1 has rank \(0\).
Complex multiplication
The elliptic curves in class 1288c do not have complex multiplication.Modular form 1288.2.a.c
sage: E.q_eigenform(10)