Properties

Label 187200mp
Number of curves $6$
Conductor $187200$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("187200.jc1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 187200mp

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
187200.jc6 187200mp1 [0, 0, 0, 215700, -15442000] [2] 2359296 \(\Gamma_0(N)\)-optimal
187200.jc5 187200mp2 [0, 0, 0, -936300, -128338000] [2, 2] 4718592  
187200.jc3 187200mp3 [0, 0, 0, -8136300, 8842862000] [2, 2] 9437184  
187200.jc2 187200mp4 [0, 0, 0, -12168300, -16324882000] [2] 9437184  
187200.jc1 187200mp5 [0, 0, 0, -129816300, 569300942000] [2] 18874368  
187200.jc4 187200mp6 [0, 0, 0, -1656300, 22541582000] [2] 18874368  

Rank

sage: E.rank()
 

The elliptic curves in class 187200mp have rank \(1\).

Modular form 187200.2.a.jc

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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.