Genus 2 Isogeny Class 1549.a

• Label: 1549.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

Genus 2 curves in isogeny class 1549.a

Label	Equation
1549.a.1549.1	\(y^2 + (x^3 + x + 1)y = -x^5 + x^3 - 3x\)

L-function data

Analytic rank:

\(1\)

Bad L-factors:

Prime	L-Factor
\(1549\)	\( ( 1 - T )( 1 - 21 T + 1549 T^{2} )\)

Good L-factors:

Prime	L-Factor
\(2\)	\( 1 + T + 3 T^{2} + 2 T^{3} + 4 T^{4}\)
\(3\)	\( 1 + 3 T + 7 T^{2} + 9 T^{3} + 9 T^{4}\)
\(5\)	\( 1 + 2 T + 8 T^{2} + 10 T^{3} + 25 T^{4}\)
\(7\)	\( 1 + 4 T^{2} + 49 T^{4}\)
\(11\)	\( 1 - 6 T^{2} + 121 T^{4}\)
\(13\)	\( ( 1 - 3 T + 13 T^{2} )( 1 + 6 T + 13 T^{2} )\)
\(17\)	\( 1 - 2 T + 27 T^{2} - 34 T^{3} + 289 T^{4}\)
\(19\)	\( 1 - 3 T^{2} + 361 T^{4}\)
\(23\)	\( 1 - T + 3 T^{2} - 23 T^{3} + 529 T^{4}\)
\(29\)	\( 1 + 3 T^{2} + 841 T^{4}\)
$\cdots$	$\cdots$

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.