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SageMath
E = EllipticCurve("ca1")
E.isogeny_class()
Elliptic curves in class 77616ca
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
77616.g1 | 77616ca1 | \([0, 0, 0, -2621892, -1720700660]\) | \(-37811178496/2381643\) | \(-125552266342923264768\) | \([]\) | \(4451328\) | \(2.6104\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 77616ca1 has rank \(1\).
Complex multiplication
The elliptic curves in class 77616ca do not have complex multiplication.Modular form 77616.2.a.ca
sage: E.q_eigenform(10)