Show commands:
SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 6762w
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 6762.x1 | 6762w1 | \([1, 1, 1, -197, -3823]\) | \(-352263793/2313846\) | \(-5555544246\) | \([]\) | \(6048\) | \(0.55327\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 6762w1 has rank \(0\).
Complex multiplication
The elliptic curves in class 6762w do not have complex multiplication.Modular form 6762.2.a.w
sage: E.q_eigenform(10)