Properties

Label 129430.g
Number of curves $4$
Conductor $129430$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("129430.g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 129430.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
129430.g1 129430k4 [1, -1, 0, -494954, 134145210] [2] 1290240  
129430.g2 129430k3 [1, -1, 0, -162134, -23441362] [2] 1290240  
129430.g3 129430k2 [1, -1, 0, -32704, 1849260] [2, 2] 645120  
129430.g4 129430k1 [1, -1, 0, 4276, 170368] [2] 322560 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 129430.g have rank \(0\).

Modular form 129430.2.a.g

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.