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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 435120k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 435120.k1 | 435120k1 | \([0, -1, 0, -3376737016, 76029764176591]\) | \(-46164817745420862606194944/357092432226656859375\) | \(-32937068966282619033309750000\) | \([]\) | \(488968704\) | \(4.3014\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 435120k1 has rank \(1\).
Complex multiplication
The elliptic curves in class 435120k do not have complex multiplication.Modular form 435120.2.a.k
sage: E.q_eigenform(10)