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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 41650.e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
41650.e1 | 41650f1 | \([1, 0, 1, -833026, 394008948]\) | \(-709731835729/334084000\) | \(-30092621520062500000\) | \([]\) | \(1451520\) | \(2.4436\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 41650.e1 has rank \(2\).
Complex multiplication
The elliptic curves in class 41650.e do not have complex multiplication.Modular form 41650.2.a.e
sage: E.q_eigenform(10)