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SageMath
E = EllipticCurve("bm1")
E.isogeny_class()
Elliptic curves in class 208725.bm
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
208725.bm1 | 208725be1 | \([0, 1, 1, -342833, 77165369]\) | \(-6439567360/1587\) | \(-1098229416796875\) | \([]\) | \(1176000\) | \(1.8739\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 208725.bm1 has rank \(1\).
Complex multiplication
The elliptic curves in class 208725.bm do not have complex multiplication.Modular form 208725.2.a.bm
sage: E.q_eigenform(10)