Properties

Label 164730d
Number of curves $4$
Conductor $164730$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("164730.dj1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 164730d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
164730.dj3 164730d1 [1, 0, 0, -8965, 324017] [2] 327680 \(\Gamma_0(N)\)-optimal
164730.dj2 164730d2 [1, 0, 0, -14745, -146475] [2, 2] 655360  
164730.dj4 164730d3 [1, 0, 0, 57505, -1143525] [2] 1310720  
164730.dj1 164730d4 [1, 0, 0, -179475, -29237793] [2] 1310720  

Rank

sage: E.rank()
 

The elliptic curves in class 164730d have rank \(0\).

Modular form 164730.2.a.dj

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{3} + q^{4} + q^{5} + q^{6} + q^{8} + q^{9} + q^{10} - 4q^{11} + q^{12} + 2q^{13} + q^{15} + q^{16} + q^{18} - q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.