Genus 2 curves in isogeny class 38416.a
Label | Equation |
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38416.a.614656.1 | \(y^2 = x^6 - 3x^5 - x^4 + 7x^3 - x^2 - 3x + 1\) |
L-function data
Analytic rank: | \(2\) (upper bound) | ||||||||||||||||||||
Mordell-Weil rank: | \(2\) | ||||||||||||||||||||
Bad L-factors: |
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Good L-factors: |
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See L-function page for more information |
Sato-Tate group
\(\mathrm{ST} =\) $E_1$, \(\quad \mathrm{ST}^0 = \mathrm{SU}(2)\)
Decomposition of the Jacobian
Splits over \(\Q\)
Decomposes up to isogeny as the square of the elliptic curve isogeny class:
Elliptic curve isogeny class 196.a
Endomorphisms of the Jacobian
Not of \(\GL_2\)-type over \(\Q\)
Endomorphism algebra over \(\Q\):
\(\End (J_{}) \otimes \Q \) | \(\simeq\) | \(\mathrm{M}_2(\)\(\Q\)\()\) |
\(\End (J_{}) \otimes \R\) | \(\simeq\) | \(\mathrm{M}_2 (\R)\) |
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.