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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 130130r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
130130.r1 | 130130r1 | \([1, 1, 0, -577307, -256515059]\) | \(-26085462395161/19685702960\) | \(-16058232668952634160\) | \([]\) | \(3594240\) | \(2.3843\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 130130r1 has rank \(1\).
Complex multiplication
The elliptic curves in class 130130r do not have complex multiplication.Modular form 130130.2.a.r
sage: E.q_eigenform(10)