Show commands:
SageMath
E = EllipticCurve("hv1")
E.isogeny_class()
Elliptic curves in class 84672hv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 84672.x1 | 84672hv1 | \([0, 0, 0, -294, 686]\) | \(13824/7\) | \(1423082304\) | \([]\) | \(36864\) | \(0.44887\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 84672hv1 has rank \(1\).
Complex multiplication
The elliptic curves in class 84672hv do not have complex multiplication.Modular form 84672.2.a.hv
sage: E.q_eigenform(10)