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Constant Tamagawa numbers of special elliptic curves | | Luying Li
; Chang Lv
; | | Date: |
1 Jun 2021 | | Abstract: | For the elliptic curves $E_{sigma 2D} : y^2 = x^3 + sigma 2Dx$ , which has
2-isogeny curve $E’_{sigma 2D} : y^2 = x^3 -sigma 8Dx$, $sigma = pm 1, D =
p_1^{e_1}p_2^{e_2}cdots p_n^{e_n}$, where $p_i$ are different odd prime
numbers and $e_i = 1 ext{ or } 3$, we demonstrate that Tamagawa numbers of
these elliptic curves are always one or zero by the use of matrix in finite
field $mathbb F_2$. The specific number depends on the value of $sigma$. By
our proofs of these results, we find a method to quickly sieve a part of the
elliptic curves with Mordell-Weil rank zero or rank one in this form as an
application. | | Source: | arXiv, 2106.00340 | | Services: | Forum | Review | PDF | Favorites | |
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