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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 68970k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 68970.l1 | 68970k1 | \([1, 1, 0, -99428727, 381566704149]\) | \(-7424865923464408587656521/33363583883827200\) | \(-488476231643114035200\) | \([]\) | \(8870400\) | \(3.1746\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 68970k1 has rank \(1\).
Complex multiplication
The elliptic curves in class 68970k do not have complex multiplication.Modular form 68970.2.a.k
sage: E.q_eigenform(10)