Properties

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

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("1110.o1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1110o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1110.o2 1110o1 [1, 0, 0, -1, 5] [2] 80 \(\Gamma_0(N)\)-optimal
1110.o1 1110o2 [1, 0, 0, -51, 135] [2] 160  

Rank

sage: E.rank()
 

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

Modular form 1110.2.a.o

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

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.