Properties

Label 17986j
Number of curves 4
Conductor 17986
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("17986.e1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 17986j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
17986.e4 17986j1 [1, 0, 0, -1598, -15356] [2] 25344 \(\Gamma_0(N)\)-optimal
17986.e3 17986j2 [1, 0, 0, -22758, -1323044] [2] 50688  
17986.e2 17986j3 [1, 0, 0, -54498, 4891648] [2] 76032  
17986.e1 17986j4 [1, 0, 0, -59788, 3883374] [2] 152064  

Rank

sage: E.rank()
 

The elliptic curves in class 17986j have rank \(0\).

Modular form 17986.2.a.e

sage: E.q_eigenform(10)
 
\( q + q^{2} - 2q^{3} + q^{4} - 2q^{6} + 4q^{7} + q^{8} + q^{9} - 6q^{11} - 2q^{12} + 2q^{13} + 4q^{14} + q^{16} + q^{17} + q^{18} + 4q^{19} + O(q^{20}) \)

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 Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.