Properties

Label 15162.j
Number of curves $6$
Conductor $15162$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("15162.j1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 15162.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
15162.j1 15162l3 [1, 0, 1, -485192, -130122646] [2] 110592  
15162.j2 15162l5 [1, 0, 1, -329962, 72225074] [2] 221184  
15162.j3 15162l4 [1, 0, 1, -37552, -994390] [2, 2] 110592  
15162.j4 15162l2 [1, 0, 1, -30332, -2034070] [2, 2] 55296  
15162.j5 15162l1 [1, 0, 1, -1452, -47126] [2] 27648 \(\Gamma_0(N)\)-optimal
15162.j6 15162l6 [1, 0, 1, 139338, -7645454] [2] 221184  

Rank

sage: E.rank()
 

The elliptic curves in class 15162.j have rank \(1\).

Modular form 15162.2.a.j

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{3} + q^{4} - 2q^{5} - q^{6} - q^{7} - q^{8} + q^{9} + 2q^{10} - 4q^{11} + q^{12} - 6q^{13} + q^{14} - 2q^{15} + q^{16} + 2q^{17} - q^{18} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.