Genus 2 isogeny class 1062.a

• Label: 1062.a
• Conductor: $1062$
• Sato-Tate group: $\mathrm{USp}(4)$
• End⁡(JQ‾)⊗R\End(J_{\overline{\Q}}) \otimes \R: $\R$
• End⁡(JQ‾)⊗Q\End(J_{\overline{\Q}}) \otimes \Q: $\Q$
• End⁡(J)⊗Q\End(J) \otimes \Q: $\Q$
• Q‾\overline{\Q}-simple: yes
• GL2\mathrm{GL}_2-type: no

Genus 2 curves in isogeny class 1062.a

Label	Equation
1062.a.6372.1	$y^2 + (x^3 + 1)y = x^5 - x^4 + x^2 - x$

L-function data

Analytic rank:

$1$

Mordell-Weil rank:

$1$

Bad L-factors:

Prime	L-Factor
$2$	$( 1 + T )( 1 + T + 2 T^{2} )$
$3$	$1 + 3 T + 3 T^{2}$
$59$	$( 1 - T )( 1 + 8 T + 59 T^{2} )$

Good L-factors:

Prime	L-Factor
$5$	$( 1 - T + 5 T^{2} )( 1 + 4 T + 5 T^{2} )$
$7$	$1 + 3 T + 6 T^{2} + 21 T^{3} + 49 T^{4}$
$11$	$( 1 - 6 T + 11 T^{2} )( 1 + 6 T + 11 T^{2} )$
$13$	$1 + 2 T + 10 T^{2} + 26 T^{3} + 169 T^{4}$
$17$	$1 + 2 T - 6 T^{2} + 34 T^{3} + 289 T^{4}$
$19$	$1 + 3 T + 6 T^{2} + 57 T^{3} + 361 T^{4}$
$23$	$1 + 2 T + 10 T^{2} + 46 T^{3} + 529 T^{4}$
$29$	$1 - 3 T + 14 T^{2} - 87 T^{3} + 841 T^{4}$
$\cdots$	$\cdots$

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.