Properties

Label 259920gz
Number of curves $1$
Conductor $259920$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("gz1")
 
E.isogeny_class()
 

Elliptic curves in class 259920gz

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
259920.gz1 259920gz1 \([0, 0, 0, -2478987, -1604141766]\) \(-11993263569/972800\) \(-136657239588156211200\) \([]\) \(10644480\) \(2.6099\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 259920gz1 has rank \(1\).

Complex multiplication

The elliptic curves in class 259920gz do not have complex multiplication.

Modular form 259920.2.a.gz

sage: E.q_eigenform(10)
 
\(q + q^{5} + 5 q^{7} - 4 q^{11} + q^{13} + 3 q^{17} + O(q^{20})\) Copy content Toggle raw display