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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 45177.k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
45177.k1 | 45177k1 | \([1, 0, 1, -976126, 681881159]\) | \(-21390625/29403\) | \(-141386806302202014147\) | \([]\) | \(1332000\) | \(2.5590\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 45177.k1 has rank \(1\).
Complex multiplication
The elliptic curves in class 45177.k do not have complex multiplication.Modular form 45177.2.a.k
sage: E.q_eigenform(10)