Properties

Label 1110.n
Number of curves $2$
Conductor $1110$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("n1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1110.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1110.n1 1110n2 \([1, 0, 0, -7364036, -7692307440]\) \(-44164307457093068844199489/1823508000000000\) \(-1823508000000000\) \([]\) \(23760\) \(2.4147\)  
1110.n2 1110n1 \([1, 0, 0, -83396, -12375024]\) \(-64144540676215729729/28962038218752000\) \(-28962038218752000\) \([3]\) \(7920\) \(1.8654\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 1110.2.a.n

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

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.