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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 266805.r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
266805.r1 | 266805r1 | \([0, 0, 1, -16559697, -42743701058]\) | \(-1376628736/1366875\) | \(-498646574307383767216875\) | \([]\) | \(40642560\) | \(3.2430\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 266805.r1 has rank \(1\).
Complex multiplication
The elliptic curves in class 266805.r do not have complex multiplication.Modular form 266805.2.a.r
sage: E.q_eigenform(10)