Genus 2 curves in isogeny class 12544.b
Label | Equation |
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12544.b.12544.1 | \(y^2 = x^5 - 3x^3 - x^2 + x\) |
12544.b.200704.1 | \(y^2 = x^5 - 7x^4 + 8x^3 + 15x^2 + 4x\) |
12544.b.401408.1 | \(y^2 + y = 4x^6 - 4x^5 - 5x^4 - 6x^3 + 7x^2 + 7x + 5\) |
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.