Show commands:
SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 308550.p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
308550.p1 | 308550p1 | \([1, 1, 0, -1575, 17175]\) | \(390625/102\) | \(112937013750\) | \([]\) | \(399840\) | \(0.82977\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 308550.p1 has rank \(1\).
Complex multiplication
The elliptic curves in class 308550.p do not have complex multiplication.Modular form 308550.2.a.p
sage: E.q_eigenform(10)