Genus 2 curves in isogeny class 2251.a
Label | Equation |
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2251.a.2251.2 | \(y^2 + xy = x^5 + x^4 - 2x^3 - x^2 + x\) |
2251.a.2251.1 | \(y^2 + (x^3 + x^2)y = x^4 - 3x^3 - 7x^2 - 17x - 5\) |
L-function data
Analytic rank: | \(1\) | ||||||||||||||||||||||||
Mordell-Weil rank: | \(1\) | ||||||||||||||||||||||||
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.