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SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 16650bc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
16650.c1 | 16650bc1 | \([1, -1, 0, -27, 351]\) | \(-121945/2738\) | \(-49900050\) | \([]\) | \(5760\) | \(0.15791\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 16650bc1 has rank \(1\).
Complex multiplication
The elliptic curves in class 16650bc do not have complex multiplication.Modular form 16650.2.a.bc
sage: E.q_eigenform(10)