hrcak mascot   Srce   HID

Izvorni znanstveni članak
https://doi.org/10.3336/gm.47.1.06

On the family of elliptic curves Y^2=X^3-T^2X+1

Petra Tadic ; Martićeva 23, 10000 Zagreb, Croatia

Puni tekst: engleski, pdf (145 KB) str. 81-93 preuzimanja: 247* citiraj
APA 6th Edition
Tadic, P. (2012). On the family of elliptic curves Y^2=X^3-T^2X+1. Glasnik matematički, 47 (1), 81-93. https://doi.org/10.3336/gm.47.1.06
MLA 8th Edition
Tadic, Petra. "On the family of elliptic curves Y^2=X^3-T^2X+1." Glasnik matematički, vol. 47, br. 1, 2012, str. 81-93. https://doi.org/10.3336/gm.47.1.06. Citirano 17.10.2021.
Chicago 17th Edition
Tadic, Petra. "On the family of elliptic curves Y^2=X^3-T^2X+1." Glasnik matematički 47, br. 1 (2012): 81-93. https://doi.org/10.3336/gm.47.1.06
Harvard
Tadic, P. (2012). 'On the family of elliptic curves Y^2=X^3-T^2X+1', Glasnik matematički, 47(1), str. 81-93. https://doi.org/10.3336/gm.47.1.06
Vancouver
Tadic P. On the family of elliptic curves Y^2=X^3-T^2X+1. Glasnik matematički [Internet]. 2012 [pristupljeno 17.10.2021.];47(1):81-93. https://doi.org/10.3336/gm.47.1.06
IEEE
P. Tadic, "On the family of elliptic curves Y^2=X^3-T^2X+1", Glasnik matematički, vol.47, br. 1, str. 81-93, 2012. [Online]. https://doi.org/10.3336/gm.47.1.06

Sažetak
Let E be the elliptic curve over Q(T) given by the equation
E:Y2=X3-T2X+1.
We prove that the torsion subgroup of the group E(C(T)) is trivial, rankQ(T)(E)=3 and rankC(T)(E)=4. We find a parametrization of E of rank at least four over the function field Q(a,i,s,n,k) where s2=i3-a2i. From this we get a family of rank ≥ 5 over the field of rational functions in two variables and a family of rank ≥ 6 over an elliptic curve of positive rank. We also found particular elliptic curves with rank ≥ 11.

Ključne riječi
Elliptic surface; elliptic curve; parametrization; function field; rank; family of elliptic curves; torsion

Hrčak ID: 82572

URI
https://hrcak.srce.hr/82572

Posjeta: 560 *