Properties

Label 424830.gs
Number of curves $2$
Conductor $424830$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("424830.gs1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 424830.gs

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
424830.gs1 424830gs1 [1, 0, 0, -4341, -42435] [2] 946176 \(\Gamma_0(N)\)-optimal
424830.gs2 424830gs2 [1, 0, 0, 15889, -321609] [2] 1892352  

Rank

sage: E.rank()
 

The elliptic curves in class 424830.gs have rank \(0\).

Modular form 424830.2.a.gs

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

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 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.