Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("o1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1110.o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1110.o1 1110o2 \([1, 0, 0, -51, 135]\) \(14688124849/123210\) \(123210\) \([2]\) \(160\) \(-0.19763\)  
1110.o2 1110o1 \([1, 0, 0, -1, 5]\) \(-117649/11100\) \(-11100\) \([2]\) \(80\) \(-0.54420\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 1110.2.a.o

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.