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SageMath
E = EllipticCurve("cd1")
E.isogeny_class()
Elliptic curves in class 61710cd
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
61710.bv1 | 61710cd1 | \([1, 1, 1, -513345, -145404225]\) | \(-8444922396903721/253364474880\) | \(-448850622482887680\) | \([]\) | \(1209600\) | \(2.1652\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 61710cd1 has rank \(1\).
Complex multiplication
The elliptic curves in class 61710cd do not have complex multiplication.Modular form 61710.2.a.cd
sage: E.q_eigenform(10)