Show commands:
SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 117117.w
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 117117.w1 | 117117l1 | \([0, 0, 1, -49860408, -135560187630]\) | \(-3895861901277528064/1561102682139\) | \(-5493120323056972384779\) | \([]\) | \(7526400\) | \(3.1351\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 117117.w1 has rank \(0\).
Complex multiplication
The elliptic curves in class 117117.w do not have complex multiplication.Modular form 117117.2.a.w
sage: E.q_eigenform(10)