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Properties

Label 28322h
Number of curves $6$
Conductor $28322$
CM no
Rank $0$
Graph

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

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 28322h have rank \(0\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1 + T\)
\(7\)\(1\)
\(17\)\(1\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(3\) \( 1 - T + 3 T^{2}\) 1.3.ab
\(5\) \( 1 - 2 T + 5 T^{2}\) 1.5.ac
\(11\) \( 1 - T + 11 T^{2}\) 1.11.ab
\(13\) \( 1 - 5 T + 13 T^{2}\) 1.13.af
\(19\) \( 1 - 6 T + 19 T^{2}\) 1.19.ag
\(23\) \( 1 + 23 T^{2}\) 1.23.a
\(29\) \( 1 - 6 T + 29 T^{2}\) 1.29.ag
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 28322h do not have complex multiplication.

Modular form 28322.2.a.h

Copy content sage:E.q_eigenform(10)
 
\(q - q^{2} - 2 q^{3} + q^{4} + 2 q^{6} - q^{8} + q^{9} - 2 q^{12} + 4 q^{13} + q^{16} - q^{18} - 2 q^{19} + O(q^{20})\) 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 Cremona numbering.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 3 & 6 & 9 & 18 \\ 2 & 1 & 6 & 3 & 18 & 9 \\ 3 & 6 & 1 & 2 & 3 & 6 \\ 6 & 3 & 2 & 1 & 6 & 3 \\ 9 & 18 & 3 & 6 & 1 & 2 \\ 18 & 9 & 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.

Elliptic curves in class 28322h

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
28322.c5 28322h1 \([1, 0, 1, -7376, -494070]\) \(-15625/28\) \(-79513303947868\) \([2]\) \(73728\) \(1.3575\) \(\Gamma_0(N)\)-optimal
28322.c4 28322h2 \([1, 0, 1, -148986, -22132078]\) \(128787625/98\) \(278296563817538\) \([2]\) \(147456\) \(1.7041\)  
28322.c6 28322h3 \([1, 0, 1, 63429, 10324934]\) \(9938375/21952\) \(-62338430295128512\) \([2]\) \(221184\) \(1.9068\)  
28322.c3 28322h4 \([1, 0, 1, -503011, 112510710]\) \(4956477625/941192\) \(2672760198903634952\) \([2]\) \(442368\) \(2.2534\)  
28322.c2 28322h5 \([1, 0, 1, -2414746, 1448261196]\) \(-548347731625/1835008\) \(-5210983887527477248\) \([2]\) \(663552\) \(2.4561\)  
28322.c1 28322h6 \([1, 0, 1, -38666906, 92542688844]\) \(2251439055699625/25088\) \(71243920337289728\) \([2]\) \(1327104\) \(2.8027\)