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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 55506.r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
55506.r1 | 55506p1 | \([1, 0, 1, -236339, 44228528]\) | \(-2454365649169/1609674\) | \(-957471634407354\) | \([]\) | \(604800\) | \(1.8142\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 55506.r1 has rank \(1\).
Complex multiplication
The elliptic curves in class 55506.r do not have complex multiplication.Modular form 55506.2.a.r
sage: E.q_eigenform(10)