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SageMath
E = EllipticCurve("bm1")
E.isogeny_class()
Elliptic curves in class 277725bm
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
277725.bm1 | 277725bm1 | \([0, -1, 1, -811133, 318654293]\) | \(-48234496/7875\) | \(-9635922016998046875\) | \([]\) | \(5087232\) | \(2.3702\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 277725bm1 has rank \(1\).
Complex multiplication
The elliptic curves in class 277725bm do not have complex multiplication.Modular form 277725.2.a.bm
sage: E.q_eigenform(10)