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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 61710.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
61710.c1 | 61710e1 | \([1, 1, 0, -652111473, -12346546138923]\) | \(-17311437234395043487224049/27152400000000000000000\) | \(-48102132896400000000000000000\) | \([]\) | \(65116800\) | \(4.1949\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 61710.c1 has rank \(1\).
Complex multiplication
The elliptic curves in class 61710.c do not have complex multiplication.Modular form 61710.2.a.c
sage: E.q_eigenform(10)