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SageMath
E = EllipticCurve("bf1")
E.isogeny_class()
Elliptic curves in class 16650bf
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
16650.x1 | 16650bf1 | \([1, -1, 0, -1311867, 579041541]\) | \(-175362106452317/131292576\) | \(-186938062312500000\) | \([]\) | \(230400\) | \(2.2474\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 16650bf1 has rank \(1\).
Complex multiplication
The elliptic curves in class 16650bf do not have complex multiplication.Modular form 16650.2.a.bf
sage: E.q_eigenform(10)