Properties

Label 250173.j
Number of curves 6
Conductor 250173
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("250173.j1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 250173.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
250173.j1 250173j6 [1, -1, 1, -14682299, -21650372260] [2] 8847360  
250173.j2 250173j4 [1, -1, 1, -922784, -334131622] [2, 2] 4423680  
250173.j3 250173j2 [1, -1, 1, -126779, 9742538] [2, 2] 2211840  
250173.j4 250173j1 [1, -1, 1, -110534, 14167676] [2] 1105920 \(\Gamma_0(N)\)-optimal
250173.j5 250173j5 [1, -1, 1, 100651, -1035389284] [2] 8847360  
250173.j6 250173j3 [1, -1, 1, 409306, 70212926] [2] 4423680  

Rank

sage: E.rank()
 

The elliptic curves in class 250173.j have rank \(1\).

Modular form 250173.2.a.j

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

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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 4 & 8 \\ 2 & 1 & 2 & 4 & 2 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 8 & 4 & 2 & 1 & 8 & 4 \\ 4 & 2 & 4 & 8 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.