↑

Properties

Label 4032.h
Number of curves $6$
Conductor $4032$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
Copy content sage:E = EllipticCurve("h1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 4032.h have rank \(0\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1\)
\(3\)\(1\)
\(7\)\(1 + T\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(5\) \( 1 + 2 T + 5 T^{2}\) 1.5.c
\(11\) \( 1 - 4 T + 11 T^{2}\) 1.11.ae
\(13\) \( 1 - 2 T + 13 T^{2}\) 1.13.ac
\(17\) \( 1 - 6 T + 17 T^{2}\) 1.17.ag
\(19\) \( 1 + 4 T + 19 T^{2}\) 1.19.e
\(23\) \( 1 + 23 T^{2}\) 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 4032.h do not have complex multiplication.

Modular form 4032.2.a.h

Copy content sage:E.q_eigenform(10)
 
\(q - 2 q^{5} - q^{7} + 4 q^{11} + 2 q^{13} + 6 q^{17} - 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 4032.h

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4032.h1 4032h5 \([0, 0, 0, -451596, 116808176]\) \(53297461115137/147\) \(28092137472\) \([2]\) \(16384\) \(1.6632\)  
4032.h2 4032h4 \([0, 0, 0, -28236, 1823600]\) \(13027640977/21609\) \(4129544208384\) \([2, 2]\) \(8192\) \(1.3167\)  
4032.h3 4032h3 \([0, 0, 0, -22476, -1289104]\) \(6570725617/45927\) \(8776786378752\) \([2]\) \(8192\) \(1.3167\)  
4032.h4 4032h6 \([0, 0, 0, -19596, 2960624]\) \(-4354703137/17294403\) \(-3305011881443328\) \([2]\) \(16384\) \(1.6632\)  
4032.h5 4032h2 \([0, 0, 0, -2316, 9200]\) \(7189057/3969\) \(758487711744\) \([2, 2]\) \(4096\) \(0.97009\)  
4032.h6 4032h1 \([0, 0, 0, 564, 1136]\) \(103823/63\) \(-12039487488\) \([2]\) \(2048\) \(0.62351\) \(\Gamma_0(N)\)-optimal