Properties

Label 13454d
Number of curves 6
Conductor 13454
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("13454.d1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 13454d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
13454.d5 13454d1 [1, 1, 0, -500, -8932] [2] 10080 \(\Gamma_0(N)\)-optimal
13454.d4 13454d2 [1, 1, 0, -10110, -395254] [2] 20160  
13454.d6 13454d3 [1, 1, 0, 4305, 184229] [2] 30240  
13454.d3 13454d4 [1, 1, 0, -34135, 1975533] [2] 60480  
13454.d2 13454d5 [1, 1, 0, -163870, 25538292] [2] 90720  
13454.d1 13454d6 [1, 1, 0, -2624030, 1634974964] [2] 181440  

Rank

sage: E.rank()
 

The elliptic curves in class 13454d have rank \(1\).

Modular form 13454.2.a.d

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

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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 3 & 6 & 9 & 18 \\ 2 & 1 & 6 & 3 & 18 & 9 \\ 3 & 6 & 1 & 2 & 3 & 6 \\ 6 & 3 & 2 & 1 & 6 & 3 \\ 9 & 18 & 3 & 6 & 1 & 2 \\ 18 & 9 & 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.