Properties

Label 259182.fx
Number of curves $1$
Conductor $259182$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("fx1")
 
E.isogeny_class()
 

Elliptic curves in class 259182.fx

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
259182.fx1 259182fx1 \([1, -1, 1, -286388246, -1761084428507]\) \(1090718342617689660877299/68598829524107395072\) \(163377922144283708721463296\) \([]\) \(138654720\) \(3.7809\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 259182.fx1 has rank \(1\).

Complex multiplication

The elliptic curves in class 259182.fx do not have complex multiplication.

Modular form 259182.2.a.fx

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + 3 q^{5} - q^{7} + q^{8} + 3 q^{10} - 2 q^{13} - q^{14} + q^{16} - q^{17} - 7 q^{19} + O(q^{20})\) Copy content Toggle raw display