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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 82110u
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 82110.s1 | 82110u1 | \([1, 0, 1, 46826, 13756472]\) | \(11355289913493692711/88276883291730000\) | \(-88276883291730000\) | \([]\) | \(1198080\) | \(1.9331\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 82110u1 has rank \(2\).
Complex multiplication
The elliptic curves in class 82110u do not have complex multiplication.Modular form 82110.2.a.u
sage: E.q_eigenform(10)