↑

Properties

Label 116160.hi
Number of curves $8$
Conductor $116160$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
Copy content sage:E = EllipticCurve("hi1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 116160.hi have rank \(1\).

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 \(\mathbb{F}_p\)
\(7\) \( 1 + 4 T + 7 T^{2}\) 1.7.e
\(13\) \( 1 - 2 T + 13 T^{2}\) 1.13.ac
\(17\) \( 1 + 6 T + 17 T^{2}\) 1.17.g
\(19\) \( 1 - 4 T + 19 T^{2}\) 1.19.ae
\(23\) \( 1 + 23 T^{2}\) 1.23.a
\(29\) \( 1 + 6 T + 29 T^{2}\) 1.29.g
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

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

Modular form 116160.2.a.hi

Copy content sage:E.q_eigenform(10)
 
\(q + q^{3} + q^{5} - 4 q^{7} + q^{9} + 2 q^{13} + q^{15} - 6 q^{17} + 4 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrrrrrr} 1 & 4 & 2 & 12 & 3 & 6 & 4 & 12 \\ 4 & 1 & 2 & 3 & 12 & 6 & 4 & 12 \\ 2 & 2 & 1 & 6 & 6 & 3 & 2 & 6 \\ 12 & 3 & 6 & 1 & 4 & 2 & 12 & 4 \\ 3 & 12 & 6 & 4 & 1 & 2 & 12 & 4 \\ 6 & 6 & 3 & 2 & 2 & 1 & 6 & 2 \\ 4 & 4 & 2 & 12 & 12 & 6 & 1 & 3 \\ 12 & 12 & 6 & 4 & 4 & 2 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 116160.hi

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
116160.hi1 116160jn7 \([0, 1, 0, -41302785, -102182292225]\) \(16778985534208729/81000\) \(37616731029504000\) \([2]\) \(6635520\) \(2.8028\)  
116160.hi2 116160jn8 \([0, 1, 0, -3512065, -345966337]\) \(10316097499609/5859375000\) \(2721117696000000000000\) \([2]\) \(6635520\) \(2.8028\)  
116160.hi3 116160jn6 \([0, 1, 0, -2582785, -1595476225]\) \(4102915888729/9000000\) \(4179636781056000000\) \([2, 2]\) \(3317760\) \(2.4563\)  
116160.hi4 116160jn5 \([0, 1, 0, -2234305, 1284710975]\) \(2656166199049/33750\) \(15673637928960000\) \([2]\) \(2211840\) \(2.2535\)  
116160.hi5 116160jn4 \([0, 1, 0, -530625, -128321217]\) \(35578826569/5314410\) \(2468033722845757440\) \([2]\) \(2211840\) \(2.2535\)  
116160.hi6 116160jn2 \([0, 1, 0, -143425, 18892223]\) \(702595369/72900\) \(33855057926553600\) \([2, 2]\) \(1105920\) \(1.9070\)  
116160.hi7 116160jn3 \([0, 1, 0, -104705, -42711297]\) \(-273359449/1536000\) \(-713324677300224000\) \([2]\) \(1658880\) \(2.1097\)  
116160.hi8 116160jn1 \([0, 1, 0, 11455, 1452735]\) \(357911/2160\) \(-1003112827453440\) \([2]\) \(552960\) \(1.5604\) \(\Gamma_0(N)\)-optimal