Show commands:
SageMath
E = EllipticCurve("ck1")
E.isogeny_class()
Elliptic curves in class 52920ck
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 52920.ca1 | 52920ck1 | \([0, 0, 0, -8967, 340599]\) | \(-1568892672/78125\) | \(-3970653750000\) | \([]\) | \(96768\) | \(1.1786\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 52920ck1 has rank \(1\).
Complex multiplication
The elliptic curves in class 52920ck do not have complex multiplication.Modular form 52920.2.a.ck
sage: E.q_eigenform(10)