# On a theorem of Mestre and Schoof

John E. Cremona^{[1]}; Andrew V. Sutherland^{[2]}

- [1] Mathematics Institute University of Warwick Coventry CV4 7AL UK
- [2] Massachusetts Institute of Technology Department of Mathematics 77 Massachusetts Avenue Cambridge, MA 02139-4307 USA

Journal de Théorie des Nombres de Bordeaux (2010)

- Volume: 22, Issue: 2, page 353-358
- ISSN: 1246-7405

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topCremona, John E., and Sutherland, Andrew V.. "On a theorem of Mestre and Schoof." Journal de Théorie des Nombres de Bordeaux 22.2 (2010): 353-358. <http://eudml.org/doc/116407>.

@article{Cremona2010,

abstract = {A well known theorem of Mestre and Schoof implies that the order of an elliptic curve $E$ over a prime field $\mathbb\{F\}_q$ can be uniquely determined by computing the orders of a few points on $E$ and its quadratic twist, provided that $q>229$. We extend this result to all finite fields with $q>49$, and all prime fields with $q>29$.},

affiliation = {Mathematics Institute University of Warwick Coventry CV4 7AL UK; Massachusetts Institute of Technology Department of Mathematics 77 Massachusetts Avenue Cambridge, MA 02139-4307 USA},

author = {Cremona, John E., Sutherland, Andrew V.},

journal = {Journal de Théorie des Nombres de Bordeaux},

keywords = {finite field; elliptic curve},

language = {eng},

number = {2},

pages = {353-358},

publisher = {Université Bordeaux 1},

title = {On a theorem of Mestre and Schoof},

url = {http://eudml.org/doc/116407},

volume = {22},

year = {2010},

}

TY - JOUR

AU - Cremona, John E.

AU - Sutherland, Andrew V.

TI - On a theorem of Mestre and Schoof

JO - Journal de Théorie des Nombres de Bordeaux

PY - 2010

PB - Université Bordeaux 1

VL - 22

IS - 2

SP - 353

EP - 358

AB - A well known theorem of Mestre and Schoof implies that the order of an elliptic curve $E$ over a prime field $\mathbb{F}_q$ can be uniquely determined by computing the orders of a few points on $E$ and its quadratic twist, provided that $q>229$. We extend this result to all finite fields with $q>49$, and all prime fields with $q>29$.

LA - eng

KW - finite field; elliptic curve

UR - http://eudml.org/doc/116407

ER -

## References

top- René Schoof, Counting points on elliptic curves over finite fields. Journal de Théorie des Nombres de Bordeaux 7 (1995), 219–254. Zbl0852.11073MR1413578
- Andrew V. Sutherland, Order computations in generic groups. PhD thesis, M.I.T., 2007, available at http://groups.csail.mit.edu/cis/theses/sutherland-phd.pdf. MR2717420
- Lawrence C. Washington, Elliptic curves: Number theory and cryptography, 2nd ed. CRC Press, 2008. Zbl1200.11043MR2404461

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