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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 140790.r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
140790.r1 | 140790ce1 | \([1, 0, 1, 28486141, 160148154782]\) | \(7922134004705549/38919195900000\) | \(-12558745724380895906100000\) | \([]\) | \(45144000\) | \(3.4983\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 140790.r1 has rank \(1\).
Complex multiplication
The elliptic curves in class 140790.r do not have complex multiplication.Modular form 140790.2.a.r
sage: E.q_eigenform(10)