Properties

Label 66654.h
Number of curves $6$
Conductor $66654$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("66654.h1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 66654.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
66654.h1 66654j6 [1, -1, 0, -376757073, -2814630157391] [2] 17301504  
66654.h2 66654j4 [1, -1, 0, -84336453, 298119355429] [2] 8650752  
66654.h3 66654j3 [1, -1, 0, -24157413, -41574871355] [2, 2] 8650752  
66654.h4 66654j2 [1, -1, 0, -5494293, 4243088245] [2, 2] 4325376  
66654.h5 66654j1 [1, -1, 0, 599787, 366034549] [2] 2162688 \(\Gamma_0(N)\)-optimal
66654.h6 66654j5 [1, -1, 0, 29832327, -201092957159] [2] 17301504  

Rank

sage: E.rank()
 

The elliptic curves in class 66654.h have rank \(1\).

Modular form 66654.2.a.h

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{4} - 2q^{5} - q^{7} - q^{8} + 2q^{10} - 4q^{11} - 2q^{13} + q^{14} + q^{16} - 6q^{17} - 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.