## Genus 2 curves in isogeny class 400.a

Label | Equation |
---|---|

400.a.409600.1 | \(y^2 = x^6 + 4x^4 + 4x^2 + 1\) |

## L-function data

Analytic rank: | \(0\) | ||||||||||||||||||||

Mordell-Weil rank: | \(0\) | ||||||||||||||||||||

Bad L-factors: |
| ||||||||||||||||||||

Good L-factors: |
| ||||||||||||||||||||

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 20.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.