Properties

Label 5610f
Number of curves $4$
Conductor $5610$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("5610.g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 5610f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
5610.g4 5610f1 [1, 1, 0, -3547, -14819] [2] 9216 \(\Gamma_0(N)\)-optimal
5610.g2 5610f2 [1, 1, 0, -35547, 2551581] [2, 2] 18432  
5610.g1 5610f3 [1, 1, 0, -567947, 164507661] [2] 36864  
5610.g3 5610f4 [1, 1, 0, -15147, 5485101] [2] 36864  

Rank

sage: E.rank()
 

The elliptic curves in class 5610f have rank \(0\).

Modular form 5610.2.a.g

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

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.