Genus 2 curves in isogeny class 9792.a
Label | Equation |
---|---|
9792.a.9792.1 | \(y^2 + y = -6x^6 - 4x^5 - 4x^4 - 5x^3 - 2x^2 - x - 1\) |
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
\(\mathrm{ST} =\) $N(\mathrm{SU}(2)\times\mathrm{SU}(2))$, \(\quad \mathrm{ST}^0 = \mathrm{SU}(2)\times\mathrm{SU}(2)\)
Decomposition of the Jacobian
Splits over the number field \(\Q (b) \simeq \) \(\Q(\sqrt{2}) \) with defining polynomial:
\(x^{2} - 2\)
Decomposes up to isogeny as the product of the non-isogenous elliptic curve isogeny classes:
Elliptic curve isogeny class 2.2.8.1-153.2-a
Elliptic curve isogeny class 2.2.8.1-153.1-a
Endomorphisms of the Jacobian
Not of \(\GL_2\)-type over \(\Q\)
Endomorphism algebra over \(\Q\):
\(\End (J_{}) \otimes \Q \) | \(\simeq\) | \(\Q\) |
\(\End (J_{}) \otimes \R\) | \(\simeq\) | \(\R\) |
Smallest field over which all endomorphisms are defined:
Galois number field \(K = \Q (a) \simeq \) \(\Q(\sqrt{2}) \) with defining polynomial \(x^{2} - 2\)
Endomorphism algebra over \(\overline{\Q}\):
\(\End (J_{\overline{\Q}}) \otimes \Q \) | \(\simeq\) | \(\Q\) \(\times\) \(\Q\) |
\(\End (J_{\overline{\Q}}) \otimes \R\) | \(\simeq\) | \(\R \times \R\) |
More complete information on endomorphism algebras and rings can be found on the pages of the individual curves in the isogeny class.