Properties

Label 55470.u
Number of curves $2$
Conductor $55470$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("55470.u1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 55470.u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
55470.u1 55470s2 [1, 1, 1, -439176, 108261153] [2] 1064448  
55470.u2 55470s1 [1, 1, 1, -69376, -4749727] [2] 532224 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 55470.u have rank \(1\).

Modular form 55470.2.a.u

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.