Properties

Label 1110h
Number of curves $4$
Conductor $1110$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("1110.h1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1110h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1110.h3 1110h1 [1, 0, 1, -313, 2588] [6] 1008 \(\Gamma_0(N)\)-optimal
1110.h2 1110h2 [1, 0, 1, -5313, 148588] [6] 2016  
1110.h4 1110h3 [1, 0, 1, 2312, -21562] [2] 3024  
1110.h1 1110h4 [1, 0, 1, -10488, -185402] [2] 6048  

Rank

sage: E.rank()
 

The elliptic curves in class 1110h have rank \(0\).

Modular form 1110.2.a.h

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{3} + q^{4} + q^{5} - q^{6} - 4q^{7} - q^{8} + q^{9} - q^{10} + 6q^{11} + q^{12} + 2q^{13} + 4q^{14} + q^{15} + q^{16} - 6q^{17} - q^{18} + 2q^{19} + O(q^{20}) \)

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 Cremona 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 Cremona labels.