Show commands:
SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 117117.v
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 117117.v1 | 117117bj1 | \([0, 0, 1, -8821829406, 318923184026632]\) | \(127680722384510660804608/1761798128013\) | \(1047684432913740699994917\) | \([]\) | \(65015808\) | \(4.1644\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 117117.v1 has rank \(1\).
Complex multiplication
The elliptic curves in class 117117.v do not have complex multiplication.Modular form 117117.2.a.v
sage: E.q_eigenform(10)