Properties

Label 21294.q
Number of curves 6
Conductor 21294
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("21294.q1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 21294.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
21294.q1 21294o6 [1, -1, 0, -4153122, 3258731412] [2] 311040  
21294.q2 21294o5 [1, -1, 0, -259362, 51051924] [2] 155520  
21294.q3 21294o4 [1, -1, 0, -54027, 3975453] [2] 103680  
21294.q4 21294o2 [1, -1, 0, -16002, -774630] [2] 34560  
21294.q5 21294o1 [1, -1, 0, -792, -17172] [2] 17280 \(\Gamma_0(N)\)-optimal
21294.q6 21294o3 [1, -1, 0, 6813, 361557] [2] 51840  

Rank

sage: E.rank()
 

The elliptic curves in class 21294.q have rank \(0\).

Modular form 21294.2.a.q

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

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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.