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SageMath
E = EllipticCurve("bp1")
E.isogeny_class()
Elliptic curves in class 413712bp
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
413712.bp1 | 413712bp1 | \([0, 0, 0, -105456, 52552240]\) | \(-53248/459\) | \(-1118013326477438976\) | \([]\) | \(6289920\) | \(2.1458\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 413712bp1 has rank \(1\).
Complex multiplication
The elliptic curves in class 413712bp do not have complex multiplication.Modular form 413712.2.a.bp
sage: E.q_eigenform(10)