Properties

Label 187200.hh
Number of curves $6$
Conductor $187200$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("187200.hh1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 187200.hh

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
187200.hh1 187200ed6 [0, 0, 0, -129816300, -569300942000] [2] 18874368  
187200.hh2 187200ed3 [0, 0, 0, -12168300, 16324882000] [2] 9437184  
187200.hh3 187200ed4 [0, 0, 0, -8136300, -8842862000] [2, 2] 9437184  
187200.hh4 187200ed5 [0, 0, 0, -1656300, -22541582000] [2] 18874368  
187200.hh5 187200ed2 [0, 0, 0, -936300, 128338000] [2, 2] 4718592  
187200.hh6 187200ed1 [0, 0, 0, 215700, 15442000] [2] 2359296 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 187200.hh have rank \(0\).

Modular form 187200.2.a.hh

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.