Properties

Label 32674d
Number of curves 4
Conductor 32674
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("32674.d1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 32674d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
32674.d4 32674d1 [1, 1, 1, -2903, -38483] [2] 60480 \(\Gamma_0(N)\)-optimal
32674.d3 32674d2 [1, 1, 1, -41343, -3252067] [2] 120960  
32674.d2 32674d3 [1, 1, 1, -99003, 11947109] [2] 181440  
32674.d1 32674d4 [1, 1, 1, -108613, 9475417] [2] 362880  

Rank

sage: E.rank()
 

The elliptic curves in class 32674d have rank \(0\).

Modular form 32674.2.a.d

sage: E.q_eigenform(10)
 
\( q + q^{2} + 2q^{3} + q^{4} + 2q^{6} - 4q^{7} + q^{8} + q^{9} - 6q^{11} + 2q^{12} - 2q^{13} - 4q^{14} + q^{16} + q^{17} + q^{18} - 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.