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math.NT2021
A remark on prime (non)congruent numbers
Tim Evink, Jaap Top, Jakob Dirk Top
This paper discusses prime numbers that are (resp. are not) congruent numbers. Particularly the only case not fully covered by earlier results, namely primes of the form ,…
math.NT2021
Two-descent on some genus two curves
Tim Evink, Gert-Jan van der Heiden, Jaap Top
For the hyperelliptic curve C_p with equation y^2=x(x-2p)(x-p)(x+p)(x+2p) with p a prime number, we discuss bounds for the rank of its Jacobian over Q, find many cases having 2-tor…