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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 429429.u
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 429429.u1 | 429429u1 | \([1, 1, 1, -65846206, -206183599588]\) | \(-30515071121161/85766121\) | \(-88739578900503664342209\) | \([]\) | \(58506624\) | \(3.2756\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 429429.u1 has rank \(1\).
Complex multiplication
The elliptic curves in class 429429.u do not have complex multiplication.Modular form 429429.2.a.u
sage: E.q_eigenform(10)