Properties

Label 166464ck
Number of curves 6
Conductor 166464
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("166464.fv1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 166464ck

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
166464.fv5 166464ck1 [0, 0, 0, -5663244, 4810888208] [2] 7077888 \(\Gamma_0(N)\)-optimal
166464.fv4 166464ck2 [0, 0, 0, -18980364, -26249962480] [2, 2] 14155776  
166464.fv6 166464ck3 [0, 0, 0, 37617396, -152870471152] [2] 28311552  
166464.fv2 166464ck4 [0, 0, 0, -288652044, -1887523897840] [2, 2] 28311552  
166464.fv3 166464ck5 [0, 0, 0, -273670284, -2092192717552] [2] 56623104  
166464.fv1 166464ck6 [0, 0, 0, -4618380684, -120804386941168] [2] 56623104  

Rank

sage: E.rank()
 

The elliptic curves in class 166464ck have rank \(1\).

Modular form 166464.2.a.fv

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 Cremona 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 Cremona labels.