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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 55664r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
55664.bg1 | 55664r1 | \([0, 0, 0, -2058931, 1132448114]\) | \(2003092024307193/9529458688\) | \(4592153744115761152\) | \([]\) | \(2566080\) | \(2.4301\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 55664r1 has rank \(1\).
Complex multiplication
The elliptic curves in class 55664r do not have complex multiplication.Modular form 55664.2.a.r
sage: E.q_eigenform(10)