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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 254898.k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
254898.k1 | 254898k1 | \([1, -1, 0, 124794, 20317716]\) | \(30004847/42336\) | \(-303264291522247776\) | \([]\) | \(3317760\) | \(2.0401\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 254898.k1 has rank \(2\).
Complex multiplication
The elliptic curves in class 254898.k do not have complex multiplication.Modular form 254898.2.a.k
sage: E.q_eigenform(10)