Show commands:
SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 57150.bg
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
57150.bg1 | 57150by1 | \([1, -1, 1, -59180, -2681553]\) | \(80492265625/35551872\) | \(10123951050000000\) | \([]\) | \(470400\) | \(1.7669\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 57150.bg1 has rank \(1\).
Complex multiplication
The elliptic curves in class 57150.bg do not have complex multiplication.Modular form 57150.2.a.bg
sage: E.q_eigenform(10)