Properties

Label 110400fl
Number of curves $6$
Conductor $110400$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("110400.cz1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 110400fl

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
110400.cz5 110400fl1 [0, -1, 0, -672033, -232416063] [2] 1769472 \(\Gamma_0(N)\)-optimal
110400.cz4 110400fl2 [0, -1, 0, -11040033, -14115168063] [2, 2] 3538944  
110400.cz3 110400fl3 [0, -1, 0, -11328033, -13339584063] [2, 2] 7077888  
110400.cz1 110400fl4 [0, -1, 0, -176640033, -903552768063] [2] 7077888  
110400.cz6 110400fl5 [0, -1, 0, 14063967, -64656816063] [2] 14155776  
110400.cz2 110400fl6 [0, -1, 0, -41328033, 87610415937] [2] 14155776  

Rank

sage: E.rank()
 

The elliptic curves in class 110400fl have rank \(0\).

Modular form 110400.2.a.cz

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.