Properties

Label 25872cw
Number of curves 4
Conductor 25872
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("25872.ci1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 25872cw

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
25872.ci3 25872cw1 [0, 1, 0, -4328, 101940] [2] 34560 \(\Gamma_0(N)\)-optimal
25872.ci4 25872cw2 [0, 1, 0, 3512, 437492] [2] 69120  
25872.ci1 25872cw3 [0, 1, 0, -63128, -6102636] [2] 103680  
25872.ci2 25872cw4 [0, 1, 0, -31768, -12136300] [2] 207360  

Rank

sage: E.rank()
 

The elliptic curves in class 25872cw have rank \(1\).

Modular form 25872.2.a.ci

sage: E.q_eigenform(10)
 
\( q + q^{3} + q^{9} + q^{11} + 4q^{13} + 6q^{17} - 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.