Properties

Label 88200gu
Number of curves $6$
Conductor $88200$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("88200.hg1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 88200gu

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
88200.hg4 88200gu1 [0, 0, 0, -1933050, 1034445125] [2] 1179648 \(\Gamma_0(N)\)-optimal
88200.hg3 88200gu2 [0, 0, 0, -1988175, 972319250] [2, 2] 2359296  
88200.hg5 88200gu3 [0, 0, 0, 2642325, 4829525750] [2] 4718592  
88200.hg2 88200gu4 [0, 0, 0, -7500675, -6860943250] [2, 2] 4718592  
88200.hg6 88200gu5 [0, 0, 0, 12344325, -37005498250] [2] 9437184  
88200.hg1 88200gu6 [0, 0, 0, -115545675, -478045188250] [2] 9437184  

Rank

sage: E.rank()
 

The elliptic curves in class 88200gu have rank \(0\).

Modular form 88200.2.a.hg

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

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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.