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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 1288e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1288.e1 | 1288e1 | \([0, 1, 0, -28, 49]\) | \(-157216000/1127\) | \(-18032\) | \([]\) | \(96\) | \(-0.35091\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 1288e1 has rank \(1\).
Complex multiplication
The elliptic curves in class 1288e do not have complex multiplication.Modular form 1288.2.a.e
sage: E.q_eigenform(10)