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SageMath
E = EllipticCurve("bm1")
E.isogeny_class()
Elliptic curves in class 188760.bm
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
188760.bm1 | 188760ch1 | \([0, -1, 0, -104705, 445604997]\) | \(-2313389056/1561572675\) | \(-85692664630573228800\) | \([]\) | \(4730880\) | \(2.5038\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 188760.bm1 has rank \(1\).
Complex multiplication
The elliptic curves in class 188760.bm do not have complex multiplication.Modular form 188760.2.a.bm
sage: E.q_eigenform(10)