Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("164730.cc1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 164730.cc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
164730.cc1 164730x3 [1, 1, 1, -878566, 316597769] [2] 1966080  
164730.cc2 164730x4 [1, 1, 1, -63586, 3257033] [2] 1966080  
164730.cc3 164730x2 [1, 1, 1, -54916, 4928609] [2, 2] 983040  
164730.cc4 164730x1 [1, 1, 1, -2896, 101153] [2] 491520 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Modular form 164730.2.a.cc

sage: E.q_eigenform(10)
 
\( q + q^{2} - q^{3} + q^{4} - q^{5} - q^{6} - 4q^{7} + q^{8} + q^{9} - q^{10} + 4q^{11} - q^{12} - 2q^{13} - 4q^{14} + q^{15} + q^{16} + q^{18} - q^{19} + O(q^{20}) \)

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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.