Genus 2 curves in isogeny class 688.a
Label | Equation |
---|---|
688.a.2752.1 | \(y^2 + y = 2x^5 - 5x^4 + 4x^3 - x\) |
688.a.704512.2 | \(y^2 = 2x^5 - 7x^4 - 8x^3 + 2x^2 + 4x + 1\) |
688.a.704512.1 | \(y^2 = 2x^5 + 4x^3 + x^2 + 2x + 1\) |
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
\(\mathrm{ST} =\) $\mathrm{USp}(4)$
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.