Properties

Label 111090o
Number of curves $4$
Conductor $111090$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more about

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

Elliptic curves in class 111090o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
111090.p3 111090o1 [1, 1, 0, -1862, 18756] [2] 180224 \(\Gamma_0(N)\)-optimal
111090.p2 111090o2 [1, 1, 0, -12442, -525056] [2, 2] 360448  
111090.p4 111090o3 [1, 1, 0, 3428, -1753394] [2] 720896  
111090.p1 111090o4 [1, 1, 0, -197592, -33889086] [2] 720896  

Rank

sage: E.rank()
 

The elliptic curves in class 111090o have rank \(0\).

Complex multiplication

The elliptic curves in class 111090o do not have complex multiplication.

Modular form 111090.2.a.o

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

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.