Properties

Label 143745.j
Number of curves 4
Conductor 143745
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("143745.j1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 143745.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
143745.j1 143745g4 [1, 0, 0, -154041, -23281500] [2] 829440  
143745.j2 143745g2 [1, 0, 0, -10296, -311049] [2, 2] 414720  
143745.j3 143745g1 [1, 0, 0, -3451, 73640] [2] 207360 \(\Gamma_0(N)\)-optimal
143745.j4 143745g3 [1, 0, 0, 23929, -1933314] [2] 829440  

Rank

sage: E.rank()
 

The elliptic curves in class 143745.j have rank \(1\).

Modular form 143745.2.a.j

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.