Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("cg1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 259182.cg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
259182.cg1 259182cg1 \([1, -1, 0, -22776, 1328894]\) \(-548643372651/81634\) \(-194423044662\) \([]\) \(552960\) \(1.1797\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 259182.cg1 has rank \(1\).

Complex multiplication

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

Modular form 259182.2.a.cg

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