Show commands:
SageMath
E = EllipticCurve("kr1")
E.isogeny_class()
Elliptic curves in class 487872kr
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 487872.kr1 | 487872kr1 | \([0, 0, 0, -132, -418]\) | \(1216512/343\) | \(71717184\) | \([]\) | \(92160\) | \(0.21427\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 487872kr1 has rank \(1\).
Complex multiplication
The elliptic curves in class 487872kr do not have complex multiplication.Modular form 487872.2.a.kr
sage: E.q_eigenform(10)