Properties

Label 23826.z
Number of curves 4
Conductor 23826
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("23826.z1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 23826.z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
23826.z1 23826y3 [1, 1, 1, -29068, 1888109] [2] 82944  
23826.z2 23826y4 [1, 1, 1, -14628, 3782637] [2] 165888  
23826.z3 23826y1 [1, 1, 1, -1993, -33133] [2] 27648 \(\Gamma_0(N)\)-optimal
23826.z4 23826y2 [1, 1, 1, 1617, -135657] [2] 55296  

Rank

sage: E.rank()
 

The elliptic curves in class 23826.z have rank \(1\).

Modular form 23826.2.a.z

sage: E.q_eigenform(10)
 
\( q + q^{2} - q^{3} + q^{4} - q^{6} + 2q^{7} + q^{8} + q^{9} - q^{11} - q^{12} + 4q^{13} + 2q^{14} + q^{16} - 6q^{17} + q^{18} + O(q^{20}) \)

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 LMFDB 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 LMFDB labels.