Show commands:
SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 121242.bc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
121242.bc1 | 121242y1 | \([1, 1, 1, -24384, -1475451]\) | \(905072904217/198396\) | \(351470616156\) | \([]\) | \(276480\) | \(1.2093\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 121242.bc1 has rank \(1\).
Complex multiplication
The elliptic curves in class 121242.bc do not have complex multiplication.Modular form 121242.2.a.bc
sage: E.q_eigenform(10)