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SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 11200bc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
11200.br1 | 11200bc1 | \([0, 0, 0, -500, 5000]\) | \(-34560/7\) | \(-2800000000\) | \([]\) | \(5760\) | \(0.53522\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 11200bc1 has rank \(0\).
Complex multiplication
The elliptic curves in class 11200bc do not have complex multiplication.Modular form 11200.2.a.bc
sage: E.q_eigenform(10)