Properties

Label 424830x
Number of curves $4$
Conductor $424830$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("x1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 424830x

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
424830.x3 424830x1 [1, 1, 0, -49858, 2684452] [2] 3538944 \(\Gamma_0(N)\)-optimal
424830.x2 424830x2 [1, 1, 0, -333078, -72142272] [2, 2] 7077888  
424830.x4 424830x3 [1, 1, 0, 91752, -243008898] [2] 14155776  
424830.x1 424830x4 [1, 1, 0, -5289428, -4684521582] [2] 14155776  

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 424830x do not have complex multiplication.

Modular form 424830.2.a.x

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

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 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.