Genus 2 isogeny class 3792.b

• Label: 3792.b
• Conductor: $3792$
• Sato-Tate group: $\mathrm{USp}(4)$
• \(\End(J_{\overline{\Q}}) \otimes \R\): \(\R\)
• \(\End(J_{\overline{\Q}}) \otimes \Q\): \(\Q\)
• \(\End(J) \otimes \Q\): \(\Q\)
• \(\overline{\Q}\)-simple: yes
• \(\mathrm{GL}_2\)-type: no

Genus 2 curves in isogeny class 3792.b

Label	Equation
3792.b.15168.1	\(y^2 + (x^3 + x)y = -3x^4 - x^3 + 6x^2 + 3x - 3\)
3792.b.485376.1	\(y^2 + (x + 1)y = 56x^6 + 8x^5 - 67x^4 - 7x^3 + 27x^2 + x - 4\)

L-function data

Analytic rank:

\(0\)

Mordell-Weil rank:

\(0\)

Bad L-factors:

Prime	L-Factor
\(2\)	\( 1 - T\)
\(3\)	\( ( 1 - T )( 1 + T + 3 T^{2} )\)
\(79\)	\( ( 1 - T )( 1 + 79 T^{2} )\)

Good L-factors:

Prime	L-Factor
\(5\)	\( ( 1 - T + 5 T^{2} )( 1 + 2 T + 5 T^{2} )\)
\(7\)	\( ( 1 - 3 T + 7 T^{2} )( 1 + 4 T + 7 T^{2} )\)
\(11\)	\( 1 - 2 T^{2} + 121 T^{4}\)
\(13\)	\( ( 1 - 3 T + 13 T^{2} )( 1 + 6 T + 13 T^{2} )\)
\(17\)	\( 1 + 2 T + 14 T^{2} + 34 T^{3} + 289 T^{4}\)
\(19\)	\( 1 - 2 T + 18 T^{2} - 38 T^{3} + 361 T^{4}\)
\(23\)	\( 1 - 6 T + 14 T^{2} - 138 T^{3} + 529 T^{4}\)
\(29\)	\( 1 - 2 T - 2 T^{2} - 58 T^{3} + 841 T^{4}\)
$\cdots$	$\cdots$

See L-function page for more information

Sato-Tate group

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

Decomposition of the Jacobian

Simple over \(\overline{\Q}\)

Endomorphisms of the Jacobian

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

Endomorphism algebra over \(\Q\):

\(\End (J_{}) \otimes \Q \)	\(\simeq\)	\(\Q\)
\(\End (J_{}) \otimes \R\)	\(\simeq\)	\(\R\)

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.