Show commands:
SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 55545p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
55545.a1 | 55545p1 | \([0, 1, 1, -2502346, -1463441240]\) | \(22128056725504/1004653125\) | \(78675376084385653125\) | \([]\) | \(3532800\) | \(2.5797\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 55545p1 has rank \(0\).
Complex multiplication
The elliptic curves in class 55545p do not have complex multiplication.Modular form 55545.2.a.p
sage: E.q_eigenform(10)