Properties

Label 32490.n
Number of curves 8
Conductor 32490
CM no
Rank 2
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("32490.n1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 32490.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
32490.n1 32490ba7 [1, -1, 0, -17328609, -27760411787] [2] 1327104  
32490.n2 32490ba8 [1, -1, 0, -1473489, -93331355] [2] 1327104  
32490.n3 32490ba6 [1, -1, 0, -1083609, -433072787] [2, 2] 663552  
32490.n4 32490ba5 [1, -1, 0, -937404, 349562578] [2] 442368  
32490.n5 32490ba4 [1, -1, 0, -222624, -34768130] [2] 442368  
32490.n6 32490ba2 [1, -1, 0, -60174, 5162080] [2, 2] 221184  
32490.n7 32490ba3 [1, -1, 0, -43929, -11586515] [2] 331776  
32490.n8 32490ba1 [1, -1, 0, 4806, 392548] [2] 110592 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 32490.n have rank \(2\).

Modular form 32490.2.a.n

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{4} + q^{5} - 4q^{7} - q^{8} - q^{10} - 2q^{13} + 4q^{14} + q^{16} - 6q^{17} + O(q^{20}) \)

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 LMFDB numbering.

\(\left(\begin{array}{rrrrrrrr} 1 & 4 & 2 & 12 & 3 & 6 & 4 & 12 \\ 4 & 1 & 2 & 3 & 12 & 6 & 4 & 12 \\ 2 & 2 & 1 & 6 & 6 & 3 & 2 & 6 \\ 12 & 3 & 6 & 1 & 4 & 2 & 12 & 4 \\ 3 & 12 & 6 & 4 & 1 & 2 & 12 & 4 \\ 6 & 6 & 3 & 2 & 2 & 1 & 6 & 2 \\ 4 & 4 & 2 & 12 & 12 & 6 & 1 & 3 \\ 12 & 12 & 6 & 4 & 4 & 2 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.