Properties

Label 110400dq
Number of curves $6$
Conductor $110400$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("110400.gx1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 110400dq

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
110400.gx5 110400dq1 [0, 1, 0, -672033, 232416063] [2] 1769472 \(\Gamma_0(N)\)-optimal
110400.gx4 110400dq2 [0, 1, 0, -11040033, 14115168063] [2, 2] 3538944  
110400.gx3 110400dq3 [0, 1, 0, -11328033, 13339584063] [2, 2] 7077888  
110400.gx1 110400dq4 [0, 1, 0, -176640033, 903552768063] [2] 7077888  
110400.gx6 110400dq5 [0, 1, 0, 14063967, 64656816063] [2] 14155776  
110400.gx2 110400dq6 [0, 1, 0, -41328033, -87610415937] [2] 14155776  

Rank

sage: E.rank()
 

The elliptic curves in class 110400dq have rank \(1\).

Modular form 110400.2.a.gx

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

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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 2 & 2 \\ 4 & 2 & 4 & 1 & 8 & 8 \\ 8 & 4 & 2 & 8 & 1 & 4 \\ 8 & 4 & 2 & 8 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.