Properties

Label 1110.a
Number of curves $4$
Conductor $1110$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("1110.a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1110.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1110.a1 1110c3 [1, 1, 0, -358318108, -2610814913072] [2] 197120  
1110.a2 1110c2 [1, 1, 0, -22394908, -40800879152] [2, 2] 98560  
1110.a3 1110c4 [1, 1, 0, -22016028, -42247518768] [2] 197120  
1110.a4 1110c1 [1, 1, 0, -1423388, -615252528] [2] 49280 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 1110.a have rank \(1\).

Modular form 1110.2.a.a

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.