Properties

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

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Show commands for: SageMath

sage: E = EllipticCurve("25872.be1")
sage: E.isogeny_class()

Elliptic curves in class 25872bk

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
25872.be3 25872bk1 [0, -1, 0, -5112, -137808] 2 27648 \(\Gamma_0(N)\)-optimal
25872.be2 25872bk2 [0, -1, 0, -9032, 106800] 4 55296  
25872.be4 25872bk3 [0, -1, 0, 34088, 796720] 2 110592  
25872.be1 25872bk4 [0, -1, 0, -114872, 15009072] 2 110592  

Rank

sage: E.rank()

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

Modular form 25872.2.a.be

sage: E.q_eigenform(10)
\( q - q^{3} + 2q^{5} + q^{9} - q^{11} + 2q^{13} - 2q^{15} + 2q^{17} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.