Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("259920.gy1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 259920gy

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
259920.gy2 259920gy1 [0, 0, 0, -122865267, 26558637874] [2] 112066560 \(\Gamma_0(N)\)-optimal
259920.gy1 259920gy2 [0, 0, 0, -1387116147, 19834082875186] [2] 224133120  

Rank

sage: E.rank()
 

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

Modular form 259920.2.a.gy

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

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 Cremona 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 Cremona labels.