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Properties

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

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

Elliptic curves in class 1110.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1110.a1 1110c3 \([1, 1, 0, -358318108, -2610814913072]\) \(5087799435928552778197163696329/125914832087040\) \(125914832087040\) \([2]\) \(197120\) \(3.1512\)  
1110.a2 1110c2 \([1, 1, 0, -22394908, -40800879152]\) \(1242142983306846366056931529/6179359141291622400\) \(6179359141291622400\) \([2, 2]\) \(98560\) \(2.8046\)  
1110.a3 1110c4 \([1, 1, 0, -22016028, -42247518768]\) \(-1180159344892952613848670409/87759036144023189760000\) \(-87759036144023189760000\) \([2]\) \(197120\) \(3.1512\)  
1110.a4 1110c1 \([1, 1, 0, -1423388, -615252528]\) \(318929057401476905525449/21353131537921474560\) \(21353131537921474560\) \([2]\) \(49280\) \(2.4580\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 1110.a do not have complex multiplication.

Modular form 1110.2.a.a

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

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.