Properties

Label 100293.a
Sato-Tate group $\mathrm{USp}(4)$
\(\End(J_{\overline{\Q}}) \otimes \R\) \(\R\)
\(\End(J_{\overline{\Q}}) \otimes \Q\) \(\Q\)
\(\overline{\Q}\)-simple yes
\(\mathrm{GL}_2\)-type no

Related objects

Learn more about

Genus 2 curves in isogeny class 100293.a

Label Equation
100293.a.902637.1 \(y^2 + (x^3 + x + 1)y = -x^6 + x^5 - 5x^4 + 3x^3 - 7x^2 + 2x - 2\)

L-function data

Analytic rank:\(0\)
 
Bad L-factors:
Prime L-Factor
\(3\)\( ( 1 - T )( 1 + T + 3 T^{2} )\)
\(101\)\( ( 1 + T )( 1 + 101 T^{2} )\)
\(331\)\( ( 1 - T )( 1 - 5 T + 331 T^{2} )\)
 
Good L-factors:
Prime L-Factor
\(2\)\( 1 - T + T^{2} - 2 T^{3} + 4 T^{4}\)
\(5\)\( ( 1 - 4 T + 5 T^{2} )( 1 + 5 T^{2} )\)
\(7\)\( ( 1 - 3 T + 7 T^{2} )( 1 + 4 T + 7 T^{2} )\)
\(11\)\( 1 - 2 T + 10 T^{2} - 22 T^{3} + 121 T^{4}\)
\(13\)\( 1 - 2 T - 7 T^{2} - 26 T^{3} + 169 T^{4}\)
\(17\)\( 1 - 6 T + 25 T^{2} - 102 T^{3} + 289 T^{4}\)
\(19\)\( ( 1 - T + 19 T^{2} )( 1 + 4 T + 19 T^{2} )\)
\(23\)\( 1 - 17 T^{2} + 529 T^{4}\)
\(29\)\( ( 1 - 9 T + 29 T^{2} )( 1 + 7 T + 29 T^{2} )\)
$\cdots$$\cdots$
 
See L-function page for more information

Sato-Tate group

\(\mathrm{ST} =\) $\mathrm{USp}(4)$

Endomorphisms of the Jacobian

Not of \(\GL_2\)-type over \(\Q\)

All \(\overline{\Q}\)-endomorphisms of the Jacobian are defined over \(\Q\).

More complete information on endomorphism algebras and rings can be found on the pages of the individual curves in the isogeny class.