Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("1110.g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1110f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1110.g3 1110f1 [1, 0, 1, -195139, 33162686] [2] 5760 \(\Gamma_0(N)\)-optimal
1110.g2 1110f2 [1, 0, 1, -195459, 33048382] [2, 2] 11520  
1110.g1 1110f3 [1, 0, 1, -320459, -14401618] [2] 23040  
1110.g4 1110f4 [1, 0, 1, -75579, 73184206] [2] 23040  

Rank

sage: E.rank()
 

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

Modular form 1110.2.a.g

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

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.