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ANTS
2006
Springer
99views Algorithms» more  ANTS 2006»
14 years 1 months ago
The Asymptotics of Points of Bounded Height on Diagonal Cubic and Quartic Threefolds
For the families ax4 = by4 +z4 +v4 +w4 , a, b = 1, . . . , 100, and ax3 = by3 + z3 + v3 + w3 , a, b = 1, . . . , 100, of projective algebraic threefolds, we test numerically the co...
Andreas-Stephan Elsenhans, Jörg Jahnel
ANTS
2006
Springer
95views Algorithms» more  ANTS 2006»
14 years 1 months ago
Constructing Pairing-Friendly Elliptic Curves with Embedding Degree 10
We present a general framework for constructing families of elliptic curves of prime order with prescribed embedding degree. We demonstrate this method by constructing curves with ...
David Freeman
ANTS
2006
Springer
93views Algorithms» more  ANTS 2006»
14 years 1 months ago
Classification of Genus 3 Curves in Special Strata of the Moduli Space
Abstract. We describe the invariants of plane quartic curves -- nonhyperelliptic genus 3 curves in their canonical model -- as determined by Dixmier and Ohno, with application to t...
Martine Girard, David R. Kohel
ANTS
2008
Springer
108views Algorithms» more  ANTS 2008»
14 years 3 days ago
Some Improvements to 4-Descent on an Elliptic Curve
The theory of 4-descent on elliptic curves has been developed in the PhD theses of Siksek [18], Womack [21] and Stamminger [20]. Prompted by our use of 4-descent in the search for ...
Tom Fisher
ANTS
2008
Springer
106views Algorithms» more  ANTS 2008»
14 years 3 days ago
Computing in Component Groups of Elliptic Curves
Let K be a p-adic local field and E an elliptic curve defined over K. The component group of E is the group E(K)/E0(K), where E0(K) denotes the subgroup of points of good reduction...
J. E. Cremona