Properties

Label 177450fb
Number of curves $8$
Conductor $177450$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("fb1")
 
E.isogeny_class()
 

Elliptic curves in class 177450fb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
177450.gh7 177450fb1 \([1, 1, 1, 887162, 242726531]\) \(1023887723039/928972800\) \(-70062097996800000000\) \([2]\) \(7077888\) \(2.4953\) \(\Gamma_0(N)\)-optimal
177450.gh6 177450fb2 \([1, 1, 1, -4520838, 2167974531]\) \(135487869158881/51438240000\) \(3879414996502500000000\) \([2, 2]\) \(14155776\) \(2.8419\)  
177450.gh4 177450fb3 \([1, 1, 1, -63670838, 195470174531]\) \(378499465220294881/120530818800\) \(9090300640018893750000\) \([2]\) \(28311552\) \(3.1885\)  
177450.gh5 177450fb4 \([1, 1, 1, -31898838, -67810193469]\) \(47595748626367201/1215506250000\) \(91672132922753906250000\) \([2, 2]\) \(28311552\) \(3.1885\)  
177450.gh8 177450fb5 \([1, 1, 1, 5365662, -216719135469]\) \(226523624554079/269165039062500\) \(-20300128641128540039062500\) \([2]\) \(56623104\) \(3.5350\)  
177450.gh2 177450fb6 \([1, 1, 1, -507211338, -4396956443469]\) \(191342053882402567201/129708022500\) \(9782435162112539062500\) \([2, 2]\) \(56623104\) \(3.5350\)  
177450.gh3 177450fb7 \([1, 1, 1, -504042588, -4454602343469]\) \(-187778242790732059201/4984939585440150\) \(-375958613366543515333593750\) \([2]\) \(113246208\) \(3.8816\)  
177450.gh1 177450fb8 \([1, 1, 1, -8115380088, -281395164293469]\) \(783736670177727068275201/360150\) \(27162113458593750\) \([2]\) \(113246208\) \(3.8816\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 177450.2.a.fb

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} - q^{6} - q^{7} + q^{8} + q^{9} + 4 q^{11} - q^{12} - q^{14} + q^{16} - 2 q^{17} + q^{18} - 4 q^{19} + O(q^{20})\) Copy content Toggle raw display

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.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 4 & 8 & 8 & 16 & 16 \\ 2 & 1 & 2 & 2 & 4 & 4 & 8 & 8 \\ 4 & 2 & 1 & 4 & 8 & 8 & 16 & 16 \\ 4 & 2 & 4 & 1 & 2 & 2 & 4 & 4 \\ 8 & 4 & 8 & 2 & 1 & 4 & 8 & 8 \\ 8 & 4 & 8 & 2 & 4 & 1 & 2 & 2 \\ 16 & 8 & 16 & 4 & 8 & 2 & 1 & 4 \\ 16 & 8 & 16 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.