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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 29624k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 29624.a1 | 29624k1 | \([0, 0, 0, 12920825, 452803434067]\) | \(100718081964000000/37453512751940327\) | \(-88711424902501164518331248\) | \([]\) | \(12925440\) | \(3.6581\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 29624k1 has rank \(1\).
Complex multiplication
The elliptic curves in class 29624k do not have complex multiplication.Modular form 29624.2.a.k
sage: E.q_eigenform(10)