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DECOMPOSITION OF THE JACOBIAN OF SOME TWISTS OF A GENUS $2$ CURVE

Part of: Arithmetic algebraic geometry

Published online by Cambridge University Press:  04 October 2024

KEUNYOUNG JEONG Open the ORCID record for KEUNYOUNG JEONG [Opens in a new window] ,
YEONG-WOOK KWON Open the ORCID record for YEONG-WOOK KWON [Opens in a new window]  and
JUNYEONG PARK Open the ORCID record for JUNYEONG PARK [Opens in a new window]
KEUNYOUNG JEONG
Affiliation:
Department of Mathematics Education, Chonnam National University, 77, Yongbong-ro, Buk-gu, Gwangju 61186, Korea e-mail: [email protected]
YEONG-WOOK KWON
Affiliation:
Department of Mathematical Sciences, Ulsan National Institute of Science and Technology, UNIST-gil 50, Ulsan 44919, Korea e-mail: [email protected]
JUNYEONG PARK*
Affiliation:
Department of Mathematics Education, Chonnam National University, 77, Yongbong-ro, Buk-gu, Gwangju 61186, Korea
*
e-mail: [email protected]
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Abstract

Cardona and Lario [‘Twists of the genus 2 curve $y^2 = x^6+1$’, J. Number Theory 209 (2020), 195–211] gave a complete classification of the twists of the curve $y^2 = x^6+1$. In this paper, we study the twists of the curve whose automorphism group is defined over a biquadratic extension of the rationals. If the twists are of type B or C in the Cardona–Lario classification, we find a pair of elliptic curves whose product is isogenous with the Jacobian of the twist.

Keywords

twistsJacobianL-function

MSC classification

Primary: 11G10: Abelian varieties of dimension $> 1$
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , First View , pp. 1 - 15
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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Footnotes

K. Jeong was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (RS-2024-00341372). Y.-W. Kwon was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2022R1I1A1A01067581). J. Park was supported by Samsung Science and Technology Foundation under Project Number SSTF-BA2001-02 and the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (RS-2024-00449679).

References

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