scholarly journals Reduction of Elliptic Curves in Equal Characteristic 3 (and 2)

2005 ◽  
Vol 48 (3) ◽  
pp. 428-444
Author(s):  
Roland Miyamoto ◽  
Jaap Top
Keyword(s):  
Elliptic Curves ◽  
Fibre Type ◽  
Valued Fields ◽  
Characteristic 2 ◽  
Characteristic 3

AbstractWe determine conductor exponent, minimal discriminant and fibre type for elliptic curves over discrete valued fields of equal characteristic 3. Along the same lines, partial results are obtained in equal characteristic 2.

Faster MapToPoint on Supersingular Elliptic Curves in Characteristic 3

2011 ◽  
Vol E94-A (1) ◽  
pp. 150-155 ◽  
Author(s):  
Yuto KAWAHARA ◽  
Tetsutaro KOBAYASHI ◽  
Gen TAKAHASHI ◽  
Tsuyoshi TAKAGI
Keyword(s):  
Elliptic Curves ◽  
Supersingular Elliptic Curves ◽  
Characteristic 3

Order counting of elliptic curves defined over finite fields of characteristic 2

2001 ◽  
Vol 85 (1) ◽  
pp. 62-70
Author(s):  
Tetsuya Izu ◽  
Jun Kogure ◽  
Masayuki Noro ◽  
Kazuhiro Yokoyama
Keyword(s):  
Elliptic Curves ◽  
Finite Fields ◽  
Characteristic 2

scholarly journals Semistable models of elliptic curves over residue characteristic 2

2020 ◽  
pp. 1-9
Author(s):  
Jeffrey Yelton
Keyword(s):  
Elliptic Curve ◽  
Elliptic Curves ◽  
Mixed Characteristic ◽  
Semistable Model ◽  
Characteristic 2 ◽  
Residue Characteristic ◽  
Legendre Form

Abstract Given an elliptic curve E in Legendre form $y^2 = x(x - 1)(x - \lambda )$ over the fraction field of a Henselian ring R of mixed characteristic $(0, 2)$ , we present an algorithm for determining a semistable model of E over R that depends only on the valuation of $\lambda $ . We provide several examples along with an easy corollary concerning $2$ -torsion.

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