Properties

Label 166464.fz
Number of curves 6
Conductor 166464
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("166464.fz1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 166464.fz

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
166464.fz1 166464gb5 [0, 0, 0, -4618380684, 120804386941168] [2] 56623104  
166464.fz2 166464gb3 [0, 0, 0, -288652044, 1887523897840] [2, 2] 28311552  
166464.fz3 166464gb6 [0, 0, 0, -273670284, 2092192717552] [2] 56623104  
166464.fz4 166464gb2 [0, 0, 0, -18980364, 26249962480] [2, 2] 14155776  
166464.fz5 166464gb1 [0, 0, 0, -5663244, -4810888208] [2] 7077888 \(\Gamma_0(N)\)-optimal
166464.fz6 166464gb4 [0, 0, 0, 37617396, 152870471152] [2] 28311552  

Rank

sage: E.rank()
 

The elliptic curves in class 166464.fz have rank \(0\).

Modular form 166464.2.a.fz

sage: E.q_eigenform(10)
 
\( q + 2q^{5} + 4q^{11} + 2q^{13} - 4q^{19} + O(q^{20}) \)

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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.