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SageMath
E = EllipticCurve("do1")
E.isogeny_class()
Elliptic curves in class 429429do
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 429429.do1 | 429429do1 | \([0, -1, 1, -118356, -15579367]\) | \(313944395776/1240029\) | \(724231359632781\) | \([]\) | \(4055040\) | \(1.7086\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 429429do1 has rank \(1\).
Complex multiplication
The elliptic curves in class 429429do do not have complex multiplication.Modular form 429429.2.a.do
sage: E.q_eigenform(10)