Properties

Label 40425k
Number of curves 6
Conductor 40425
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("40425.cl1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 40425k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
40425.cl4 40425k1 [1, 1, 0, -41675, -3291000] [2] 122880 \(\Gamma_0(N)\)-optimal
40425.cl3 40425k2 [1, 1, 0, -47800, -2268125] [2, 2] 245760  
40425.cl6 40425k3 [1, 1, 0, 154325, -16214750] [2] 491520  
40425.cl2 40425k4 [1, 1, 0, -347925, 77265000] [2, 2] 491520  
40425.cl5 40425k5 [1, 1, 0, 37950, 239718375] [2] 983040  
40425.cl1 40425k6 [1, 1, 0, -5535800, 5010934125] [2] 983040  

Rank

sage: E.rank()
 

The elliptic curves in class 40425k have rank \(0\).

Modular form 40425.2.a.cl

sage: E.q_eigenform(10)
 
\( q + q^{2} - q^{3} - q^{4} - q^{6} - 3q^{8} + q^{9} - q^{11} + q^{12} + 6q^{13} - q^{16} + 2q^{17} + q^{18} - 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.