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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 189618.r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
189618.r1 | 189618z1 | \([1, 0, 1, -5581, 162242]\) | \(-672937149625/10996722\) | \(-314077377042\) | \([]\) | \(288000\) | \(1.0061\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 189618.r1 has rank \(2\).
Complex multiplication
The elliptic curves in class 189618.r do not have complex multiplication.Modular form 189618.2.a.r
sage: E.q_eigenform(10)