Properties

Label 110946.g
Number of curves 4
Conductor 110946
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("110946.g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 110946.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
110946.g1 110946h3 [1, 1, 0, -135355, -19150307] [2] 829440  
110946.g2 110946h4 [1, 1, 0, -68115, -38098539] [2] 1658880  
110946.g3 110946h1 [1, 1, 0, -9280, 320716] [2] 276480 \(\Gamma_0(N)\)-optimal
110946.g4 110946h2 [1, 1, 0, 7530, 1373022] [2] 552960  

Rank

sage: E.rank()
 

The elliptic curves in class 110946.g have rank \(0\).

Modular form 110946.2.a.g

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

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 LMFDB 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 LMFDB labels.