Properties

Label 37200.dc
Number of curves $6$
Conductor $37200$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("37200.dc1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 37200.dc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
37200.dc1 37200cz6 [0, 1, 0, -123008008, 525066463988] [2] 2359296  
37200.dc2 37200cz4 [0, 1, 0, -7688008, 8202223988] [2, 2] 1179648  
37200.dc3 37200cz5 [0, 1, 0, -7568008, 8470783988] [2] 2359296  
37200.dc4 37200cz3 [0, 1, 0, -1480008, -540816012] [2] 1179648  
37200.dc5 37200cz2 [0, 1, 0, -488008, 123823988] [2, 2] 589824  
37200.dc6 37200cz1 [0, 1, 0, 23992, 8111988] [2] 294912 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 37200.dc have rank \(0\).

Modular form 37200.2.a.dc

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.