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SageMath
E = EllipticCurve("bm1")
E.isogeny_class()
Elliptic curves in class 12870.bm
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
12870.bm1 | 12870bp1 | \([1, -1, 1, -9628403, 27433323987]\) | \(-135412551115258010417641/367535633653760000000\) | \(-267933476933591040000000\) | \([]\) | \(1532160\) | \(3.1828\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 12870.bm1 has rank \(0\).
Complex multiplication
The elliptic curves in class 12870.bm do not have complex multiplication.Modular form 12870.2.a.bm
sage: E.q_eigenform(10)