Properties

Label 177600ir
Number of curves $6$
Conductor $177600$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("177600.ci1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 177600ir

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
177600.ci5 177600ir1 [0, -1, 0, -1352033, 2083475937] [2] 7962624 \(\Gamma_0(N)\)-optimal
177600.ci4 177600ir2 [0, -1, 0, -34120033, 76565139937] [2, 2] 15925248  
177600.ci1 177600ir3 [0, -1, 0, -545608033, 4905523347937] [2] 31850496  
177600.ci3 177600ir4 [0, -1, 0, -46920033, 13909139937] [2, 2] 31850496  
177600.ci6 177600ir5 [0, -1, 0, 186359967, 110720339937] [4] 63700992  
177600.ci2 177600ir6 [0, -1, 0, -485000033, -4093090860063] [2] 63700992  

Rank

sage: E.rank()
 

The elliptic curves in class 177600ir have rank \(0\).

Modular form 177600.2.a.ci

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

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.