Properties

Label 259920.gw
Number of curves $2$
Conductor $259920$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("gw1")
 
E.isogeny_class()
 

Elliptic curves in class 259920.gw

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
259920.gw1 259920gw2 \([0, 0, 0, -3842427, -2891687254]\) \(306331959547531/900000000\) \(18432777830400000000\) \([2]\) \(11796480\) \(2.5669\)  
259920.gw2 259920gw1 \([0, 0, 0, -340347, -3872086]\) \(212883113611/122880000\) \(2516688599777280000\) \([2]\) \(5898240\) \(2.2203\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 259920.gw have rank \(0\).

Complex multiplication

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

Modular form 259920.2.a.gw

sage: E.q_eigenform(10)
 
\(q + q^{5} + 4 q^{7} + 6 q^{11} - 4 q^{13} - 6 q^{17} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.