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SageMath
E = EllipticCurve("bn1")
E.isogeny_class()
Elliptic curves in class 53312bn
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
53312.a1 | 53312bn1 | \([0, 0, 0, -1372, 19600]\) | \(-7260624/17\) | \(-668745728\) | \([]\) | \(73728\) | \(0.57382\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 53312bn1 has rank \(2\).
Complex multiplication
The elliptic curves in class 53312bn do not have complex multiplication.Modular form 53312.2.a.bn
sage: E.q_eigenform(10)