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SageMath
E = EllipticCurve("do1")
E.isogeny_class()
Elliptic curves in class 205350do
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 205350.p1 | 205350do1 | \([1, 1, 0, -147869825, -691802452875]\) | \(52121698757/31104\) | \(213383126825700750000000\) | \([]\) | \(37296000\) | \(3.4206\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 205350do1 has rank \(0\).
Complex multiplication
The elliptic curves in class 205350do do not have complex multiplication.Modular form 205350.2.a.do
sage: E.q_eigenform(10)