Show commands:
SageMath
E = EllipticCurve("fw1")
E.isogeny_class()
Elliptic curves in class 304704fw
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
304704.fw1 | 304704fw1 | \([0, 0, 0, -82524, 9441592]\) | \(-562432/23\) | \(-2541688576883712\) | \([]\) | \(2027520\) | \(1.7235\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 304704fw1 has rank \(1\).
Complex multiplication
The elliptic curves in class 304704fw do not have complex multiplication.Modular form 304704.2.a.fw
sage: E.q_eigenform(10)