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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 422370w
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 422370.w1 | 422370w1 | \([1, -1, 0, 3780, -713480]\) | \(1194389981/44555160\) | \(-222785201138760\) | \([]\) | \(1804800\) | \(1.4330\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 422370w1 has rank \(0\).
Complex multiplication
The elliptic curves in class 422370w do not have complex multiplication.Modular form 422370.2.a.w
sage: E.q_eigenform(10)