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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 786c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
786.e1 | 786c1 | \([1, 1, 0, 1217, 6622405]\) | \(199084633070471/18943113870853632\) | \(-18943113870853632\) | \([]\) | \(12960\) | \(1.8022\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 786c1 has rank \(1\).
Complex multiplication
The elliptic curves in class 786c do not have complex multiplication.Modular form 786.2.a.c
sage: E.q_eigenform(10)