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SageMath
E = EllipticCurve("eu1")
E.isogeny_class()
Elliptic curves in class 241200.eu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 241200.eu1 | 241200eu1 | \([0, 0, 0, -213750, -39065625]\) | \(-9481881600/300763\) | \(-34258785468750000\) | \([]\) | \(1428480\) | \(1.9488\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 241200.eu1 has rank \(1\).
Complex multiplication
The elliptic curves in class 241200.eu do not have complex multiplication.Modular form 241200.2.a.eu
sage: E.q_eigenform(10)