Show commands:
SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 249090.k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 249090.k1 | 249090k1 | \([1, 1, 0, -14922144748, 1280185258446352]\) | \(-1138767460191500803975891/1535064697265625000000\) | \(-495346493102462127685546875000000\) | \([]\) | \(1640943360\) | \(4.9662\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 249090.k1 has rank \(0\).
Complex multiplication
The elliptic curves in class 249090.k do not have complex multiplication.Modular form 249090.2.a.k
sage: E.q_eigenform(10)