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SageMath
E = EllipticCurve("cy1")
E.isogeny_class()
Elliptic curves in class 163254cy
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
163254.g1 | 163254cy1 | \([1, 1, 0, -671778, -208402956]\) | \(243202777441/5007744\) | \(690360035405878656\) | \([]\) | \(2620800\) | \(2.2134\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 163254cy1 has rank \(1\).
Complex multiplication
The elliptic curves in class 163254cy do not have complex multiplication.Modular form 163254.2.a.cy
sage: E.q_eigenform(10)