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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 69828.k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 69828.k1 | 69828b1 | \([0, -1, 0, -184776173, -35854860511095]\) | \(-34801580274688000/27682340832837603\) | \(-554964834689016527359058289408\) | \([]\) | \(58556160\) | \(4.3864\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 69828.k1 has rank \(1\).
Complex multiplication
The elliptic curves in class 69828.k do not have complex multiplication.Modular form 69828.2.a.k
sage: E.q_eigenform(10)