Improved rank bounds from 2-descent on hyperelliptic Jacobians
Brendan Creutz
TL;DR
This paper presents an enhancement to 2-descent algorithms for hyperelliptic Jacobians, leading to more accurate rank bounds that align with the conjectured parity, and implements these improvements in Magma.
Contribution
It introduces a qualitative improvement to 2-descent algorithms for hyperelliptic Jacobians and provides an implementation in Magma.
Findings
Sharper rank bounds achieved
Rank bounds now match the conjectured parity
Implementation available in Magma
Abstract
We describe a qualitative improvement to the algorithms for performing 2-descents to obtain information regarding the Mordell-Weil rank of a hyperelliptic Jacobian. The improvement has been implemented in the Magma Computational Algebra System and as a result, the rank bounds for hyperelliptic Jacobians are now sharper and have the conjectured parity.
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