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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 227430.r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
227430.r1 | 227430fk1 | \([1, -1, 0, 3858120, -2252699424]\) | \(185183253170999/171032148000\) | \(-5865795041765160852000\) | \([]\) | \(16588800\) | \(2.8642\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 227430.r1 has rank \(1\).
Complex multiplication
The elliptic curves in class 227430.r do not have complex multiplication.Modular form 227430.2.a.r
sage: E.q_eigenform(10)