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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 429429n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 429429.n1 | 429429n1 | \([0, 1, 1, -57717612, -1278086326786]\) | \(-3309867537183567872/107922634023138753\) | \(-693347103745974406176034587\) | \([]\) | \(248451840\) | \(3.8306\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 429429n1 has rank \(0\).
Complex multiplication
The elliptic curves in class 429429n do not have complex multiplication.Modular form 429429.2.a.n
sage: E.q_eigenform(10)