Properties

Label 726.i
Number of curves 4
Conductor 726
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("726.i1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 726.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
726.i1 726h3 [1, 0, 0, -9743, 367929] [2] 1440  
726.i2 726h4 [1, 0, 0, -4903, 734801] [2] 2880  
726.i3 726h1 [1, 0, 0, -668, -6324] [2] 480 \(\Gamma_0(N)\)-optimal
726.i4 726h2 [1, 0, 0, 542, -26410] [2] 960  

Rank

sage: E.rank()
 

The elliptic curves in class 726.i have rank \(0\).

Modular form 726.2.a.i

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{3} + q^{4} + q^{6} - 2q^{7} + q^{8} + q^{9} + q^{12} + 4q^{13} - 2q^{14} + q^{16} + 6q^{17} + q^{18} + 4q^{19} + O(q^{20}) \)

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 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.