Properties

Label 369600.pg
Number of curves $6$
Conductor $369600$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("369600.pg1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 369600.pg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
369600.pg1 369600pg5 [0, 1, 0, -21200033, 37562148063] [2] 25165824  
369600.pg2 369600pg3 [0, 1, 0, -1400033, 516348063] [2, 2] 12582912  
369600.pg3 369600pg2 [0, 1, 0, -432033, -102203937] [2, 2] 6291456  
369600.pg4 369600pg1 [0, 1, 0, -424033, -106419937] [2] 3145728 \(\Gamma_0(N)\)-optimal
369600.pg5 369600pg4 [0, 1, 0, 407967, -450803937] [2] 12582912  
369600.pg6 369600pg6 [0, 1, 0, 2911967, 3073364063] [2] 25165824  

Rank

sage: E.rank()
 

The elliptic curves in class 369600.pg have rank \(0\).

Modular form 369600.2.a.pg

sage: E.q_eigenform(10)
 
\( q + q^{3} - q^{7} + q^{9} + q^{11} - 2q^{13} + 6q^{17} - 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.