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Properties

Label 176610.bs
Number of curves $6$
Conductor $176610$
CM no
Rank $0$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("bs1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 176610.bs have rank \(0\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1 + T\)
\(3\)\(1 - T\)
\(5\)\(1 - T\)
\(7\)\(1 - T\)
\(29\)\(1\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(11\) \( 1 + 4 T + 11 T^{2}\) 1.11.e
\(13\) \( 1 + 2 T + 13 T^{2}\) 1.13.c
\(17\) \( 1 + 2 T + 17 T^{2}\) 1.17.c
\(19\) \( 1 - 4 T + 19 T^{2}\) 1.19.ae
\(23\) \( 1 + 8 T + 23 T^{2}\) 1.23.i
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 176610.bs do not have complex multiplication.

Modular form 176610.2.a.bs

Copy content sage:E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} + q^{5} - q^{6} + q^{7} - q^{8} + q^{9} - q^{10} - 4 q^{11} + q^{12} - 2 q^{13} - q^{14} + q^{15} + q^{16} - 2 q^{17} - q^{18} + 4 q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

Copy content 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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 176610.bs

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
176610.bs1 176610by6 \([1, 0, 1, -14128818, -20442398594]\) \(524388516989299201/3150\) \(1873693461150\) \([2]\) \(6193152\) \(2.4204\)  
176610.bs2 176610by4 \([1, 0, 1, -883068, -319455194]\) \(128031684631201/9922500\) \(5902134402622500\) \([2, 2]\) \(3096576\) \(2.0738\)  
176610.bs3 176610by5 \([1, 0, 1, -824198, -363866722]\) \(-104094944089921/35880468750\) \(-21342539580911718750\) \([2]\) \(6193152\) \(2.4204\)  
176610.bs4 176610by3 \([1, 0, 1, -311188, 63125798]\) \(5602762882081/345888060\) \(205742284543447260\) \([2]\) \(3096576\) \(2.0738\)  
176610.bs5 176610by2 \([1, 0, 1, -58888, -4288762]\) \(37966934881/8643600\) \(5141414857395600\) \([2, 2]\) \(1548288\) \(1.7273\)  
176610.bs6 176610by1 \([1, 0, 1, 8392, -413434]\) \(109902239/188160\) \(-111921956079360\) \([2]\) \(774144\) \(1.3807\) \(\Gamma_0(N)\)-optimal