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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 29760k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 29760.d1 | 29760k1 | \([0, -1, 0, 72639, -18171135]\) | \(1293532570753912/5090071640625\) | \(-166791467520000000\) | \([]\) | \(338688\) | \(1.9873\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 29760k1 has rank \(0\).
Complex multiplication
The elliptic curves in class 29760k do not have complex multiplication.Modular form 29760.2.a.k
sage: E.q_eigenform(10)