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SageMath
E = EllipticCurve("eg1")
E.isogeny_class()
Elliptic curves in class 226512.eg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 226512.eg1 | 226512cc1 | \([0, 0, 0, -23232, 4961968]\) | \(-262144/1859\) | \(-9833836357103616\) | \([]\) | \(1036800\) | \(1.7519\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 226512.eg1 has rank \(1\).
Complex multiplication
The elliptic curves in class 226512.eg do not have complex multiplication.Modular form 226512.2.a.eg
sage: E.q_eigenform(10)