Properties

Label 476.a
Conductor 476476
Sato-Tate group SU(2)×SU(2)\mathrm{SU}(2)\times\mathrm{SU}(2)
End(JQ)R\End(J_{\overline{\Q}}) \otimes \R R×R\R \times \R
End(JQ)Q\End(J_{\overline{\Q}}) \otimes \Q Q×Q\Q \times \Q
End(J)Q\End(J) \otimes \Q Q×Q\Q \times \Q
Q\overline{\Q}-simple no
GL2\mathrm{GL}_2-type yes

Related objects

Learn more

Genus 2 curves in isogeny class 476.a

Label Equation
476.a.952.1 y2+(x3+1)y=5x4+7x3+25x275x+54y^2 + (x^3 + 1)y = -5x^4 + 7x^3 + 25x^2 - 75x + 54

L-function data

Analytic rank:00
Mordell-Weil rank:00
 
Bad L-factors:
Prime L-Factor
22(1T)(1+T) ( 1 - T )( 1 + T )
77(1T)(1+4T+7T2) ( 1 - T )( 1 + 4 T + 7 T^{2} )
1717(1+T)(16T+17T2) ( 1 + T )( 1 - 6 T + 17 T^{2} )
 
Good L-factors:
Prime L-Factor
33(1+2T+3T2)2 ( 1 + 2 T + 3 T^{2} )^{2}
55(1+5T2)2 ( 1 + 5 T^{2} )^{2}
1111(16T+11T2)(1+11T2) ( 1 - 6 T + 11 T^{2} )( 1 + 11 T^{2} )
1313(12T+13T2)(1+4T+13T2) ( 1 - 2 T + 13 T^{2} )( 1 + 4 T + 13 T^{2} )
1919(12T+19T2)(1+4T+19T2) ( 1 - 2 T + 19 T^{2} )( 1 + 4 T + 19 T^{2} )
2323(1+23T2)2 ( 1 + 23 T^{2} )^{2}
2929(1+29T2)(1+6T+29T2) ( 1 + 29 T^{2} )( 1 + 6 T + 29 T^{2} )
\cdots\cdots
 
See L-function page for more information

Sato-Tate group

ST=\mathrm{ST} = SU(2)×SU(2)\mathrm{SU}(2)\times\mathrm{SU}(2), ST0=SU(2)×SU(2)\quad \mathrm{ST}^0 = \mathrm{SU}(2)\times\mathrm{SU}(2)

Decomposition of the Jacobian

Splits over Q\Q

Decomposes up to isogeny as the product of the non-isogenous elliptic curve isogeny classes:
  Elliptic curve isogeny class 14.a
  Elliptic curve isogeny class 34.a

Endomorphisms of the Jacobian

Of GL2\GL_2-type over Q\Q

Endomorphism algebra over Q\Q:

End(J)Q\End (J_{}) \otimes \Q \simeqQ\Q ×\times Q\Q
End(J)R\End (J_{}) \otimes \R\simeq R×R\R \times \R

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

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