Genus 2 curves in isogeny class 8670.b
Label | Equation |
---|---|
8670.b.312120.1 | \(y^2 + (x^2 + x)y = 5x^6 + 15x^5 + 34x^4 + 43x^3 + 42x^2 + 23x + 8\) |
L-function data
Analytic rank: | \(0\) | ||||||||||||||||
Mordell-Weil rank: | \(0\) | ||||||||||||||||
Bad L-factors: |
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Good L-factors: |
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See L-function page for more information |
Sato-Tate group
\(\mathrm{ST} =\) $\mathrm{SU}(2)\times\mathrm{SU}(2)$, \(\quad \mathrm{ST}^0 = \mathrm{SU}(2)\times\mathrm{SU}(2)\)
Decomposition of the Jacobian
Splits over \(\Q\)
Decomposes up to isogeny as the product of the non-isogenous elliptic curve isogeny classes:
Elliptic curve isogeny class 85.a
Elliptic curve isogeny class 102.b
Endomorphisms of the Jacobian
Of \(\GL_2\)-type over \(\Q\)
Endomorphism algebra over \(\Q\):
\(\End (J_{}) \otimes \Q \) | \(\simeq\) | \(\Q\) \(\times\) \(\Q\) |
\(\End (J_{}) \otimes \R\) | \(\simeq\) | \(\R \times \R\) |
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.