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SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 455175bc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
455175.bc1 | 455175bc1 | \([1, -1, 1, -2823440, -3087704968]\) | \(-1151731985/1240029\) | \(-2680030097613128576925\) | \([]\) | \(17233920\) | \(2.8066\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 455175bc1 has rank \(2\).
Complex multiplication
The elliptic curves in class 455175bc do not have complex multiplication.Modular form 455175.2.a.bc
sage: E.q_eigenform(10)