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Properties

Label 116160.fx
Number of curves $6$
Conductor $116160$
CM no
Rank $0$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("fx1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 116160.fx have rank \(0\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1\)
\(3\)\(1 - T\)
\(5\)\(1 + T\)
\(11\)\(1\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(7\) \( 1 + 7 T^{2}\) 1.7.a
\(13\) \( 1 + 2 T + 13 T^{2}\) 1.13.c
\(17\) \( 1 + 2 T + 17 T^{2}\) 1.17.c
\(19\) \( 1 - 4 T + 19 T^{2}\) 1.19.ae
\(23\) \( 1 + 23 T^{2}\) 1.23.a
\(29\) \( 1 + 2 T + 29 T^{2}\) 1.29.c
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 116160.fx do not have complex multiplication.

Modular form 116160.2.a.fx

Copy content sage:E.q_eigenform(10)
 
\(q + q^{3} - q^{5} + q^{9} - 2 q^{13} - q^{15} - 2 q^{17} + 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 116160.fx

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
116160.fx1 116160hp6 \([0, 1, 0, -30085601, -63524069985]\) \(6484907238722641/283593750\) \(131702096486400000000\) \([2]\) \(5898240\) \(2.9388\)  
116160.fx2 116160hp4 \([0, 1, 0, -9099361, 10561771295]\) \(179415687049201/1443420\) \(670330146945761280\) \([2]\) \(2949120\) \(2.5922\)  
116160.fx3 116160hp3 \([0, 1, 0, -1974881, -887763681]\) \(1834216913521/329422500\) \(152985155278602240000\) \([2, 2]\) \(2949120\) \(2.5922\)  
116160.fx4 116160hp2 \([0, 1, 0, -580961, 157397535]\) \(46694890801/3920400\) \(1820649781827993600\) \([2, 2]\) \(1474560\) \(2.2456\)  
116160.fx5 116160hp1 \([0, 1, 0, 38559, 11314719]\) \(13651919/126720\) \(-58849285877268480\) \([2]\) \(737280\) \(1.8990\) \(\Gamma_0(N)\)-optimal
116160.fx6 116160hp5 \([0, 1, 0, 3833119, -5119472481]\) \(13411719834479/32153832150\) \(-14932371056226769305600\) \([2]\) \(5898240\) \(2.9388\)