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SageMath
E = EllipticCurve("ex1")
E.isogeny_class()
Elliptic curves in class 85680ex
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
85680.ea1 | 85680ex1 | \([0, 0, 0, -685418592, 6908004458224]\) | \(-11926249134908509075308544/2246680441062421875\) | \(-6708551850125334720000000\) | \([]\) | \(24192000\) | \(3.7653\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 85680ex1 has rank \(0\).
Complex multiplication
The elliptic curves in class 85680ex do not have complex multiplication.Modular form 85680.2.a.ex
sage: E.q_eigenform(10)