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SageMath
E = EllipticCurve("bm1")
E.isogeny_class()
Elliptic curves in class 45570.bm
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
45570.bm1 | 45570bi1 | \([1, 0, 1, -9973, 432128]\) | \(-932288503609/148800000\) | \(-17506171200000\) | \([]\) | \(118800\) | \(1.2692\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 45570.bm1 has rank \(0\).
Complex multiplication
The elliptic curves in class 45570.bm do not have complex multiplication.Modular form 45570.2.a.bm
sage: E.q_eigenform(10)