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SageMath
E = EllipticCurve("dr1")
E.isogeny_class()
Elliptic curves in class 190575dr
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
190575.ej1 | 190575dr1 | \([1, -1, 0, -87665067, 316716068466]\) | \(-30515071121161/85766121\) | \(-209413562026910439515625\) | \([]\) | \(31933440\) | \(3.3472\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 190575dr1 has rank \(0\).
Complex multiplication
The elliptic curves in class 190575dr do not have complex multiplication.Modular form 190575.2.a.dr
sage: E.q_eigenform(10)