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SageMath
E = EllipticCurve("bm1")
E.isogeny_class()
Elliptic curves in class 106722bm
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
106722.i1 | 106722bm1 | \([1, -1, 0, -546849, 155701629]\) | \(3233229419/2048\) | \(11455653161981952\) | \([]\) | \(1995840\) | \(2.0227\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 106722bm1 has rank \(0\).
Complex multiplication
The elliptic curves in class 106722bm do not have complex multiplication.Modular form 106722.2.a.bm
sage: E.q_eigenform(10)