Properties

Label 177450hr
Number of curves $4$
Conductor $177450$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("hr1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 177450hr

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
177450.do3 177450hr1 [1, 0, 1, -14876, -442102] [2] 884736 \(\Gamma_0(N)\)-optimal
177450.do2 177450hr2 [1, 0, 1, -99376, 11725898] [2, 2] 1769472  
177450.do1 177450hr3 [1, 0, 1, -1578126, 762930898] [2] 3538944  
177450.do4 177450hr4 [1, 0, 1, 27374, 39610898] [2] 3538944  

Rank

sage: E.rank()
 

The elliptic curves in class 177450hr have rank \(0\).

Complex multiplication

The elliptic curves in class 177450hr do not have complex multiplication.

Modular form 177450.2.a.hr

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{3} + q^{4} - q^{6} - q^{7} - q^{8} + q^{9} + 4q^{11} + q^{12} + q^{14} + q^{16} + 6q^{17} - q^{18} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.