Show commands:
SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 201810.bc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
201810.bc1 | 201810bq1 | \([1, 0, 1, -50473, 12707756]\) | \(-15397206157321/66679200000\) | \(-61579641463200000\) | \([]\) | \(2160000\) | \(1.9066\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 201810.bc1 has rank \(1\).
Complex multiplication
The elliptic curves in class 201810.bc do not have complex multiplication.Modular form 201810.2.a.bc
sage: E.q_eigenform(10)