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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 422331x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 422331.x1 | 422331x1 | \([1, 0, 0, 6968289, 37271967732]\) | \(2307174311/38336139\) | \(-621770530321373834813139\) | \([]\) | \(50544000\) | \(3.2461\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 422331x1 has rank \(1\).
Complex multiplication
The elliptic curves in class 422331x do not have complex multiplication.Modular form 422331.2.a.x
sage: E.q_eigenform(10)