Properties

Label 14440.g
Number of curves 4
Conductor 14440
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("14440.g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 14440.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
14440.g1 14440h3 [0, 0, 0, -38627, 2921934] [2] 27648  
14440.g2 14440h2 [0, 0, 0, -2527, 41154] [2, 2] 13824  
14440.g3 14440h1 [0, 0, 0, -722, -6859] [2] 6912 \(\Gamma_0(N)\)-optimal
14440.g4 14440h4 [0, 0, 0, 4693, 233206] [2] 27648  

Rank

sage: E.rank()
 

The elliptic curves in class 14440.g have rank \(0\).

Modular form 14440.2.a.g

sage: E.q_eigenform(10)
 
\( q + q^{5} - 4q^{7} - 3q^{9} + 4q^{11} + 2q^{13} + 2q^{17} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.