Properties

Label 5610.o
Number of curves $4$
Conductor $5610$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("5610.o1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 5610.o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
5610.o1 5610n4 [1, 0, 1, -220364, -39529438] [2] 69120  
5610.o2 5610n3 [1, 0, 1, -23844, 403426] [2] 34560  
5610.o3 5610n2 [1, 0, 1, -18899, 966116] [6] 23040  
5610.o4 5610n1 [1, 0, 1, -18729, 984952] [6] 11520 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 5610.o have rank \(1\).

Modular form 5610.2.a.o

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

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 LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.