File:BSD data plot for elliptic curve 800h1.svg
Size of this PNG preview of this SVG file: 436 × 296 pixels. Other resolutions: 320 × 217 pixels | 640 × 434 pixels | 1,024 × 695 pixels | 1,280 × 869 pixels | 2,560 × 1,738 pixels.
Original file (SVG file, nominally 436 × 296 pixels, file size: 5.07 MB)
 | This is a file from the Wikimedia Commons. Information from its description page there is shown below. Commons is a freely licensed media file repository. You can help. |
Summary
This diagram was created with SageMath.
| Description |
English: A plot of the type of data used by Birch and Swinnerton-Dyer to support their conjecture. The curve in question is y2 = x3 − 5x (curve 800h1 of the Cremona database). This is a curve of rank 1 (and one of the curves originally looked at by Birch and Swinnerton-Dyer). The horizontal axis is a bound X and the vertical axis is where Np is the number of points on the curve modulo p. The scale of the horizontal axis is log(log(X)) while the scale of the vertical axis is log(Y). The data should thus resemble a line of slope 1 (equal to the rank of the curve). The data points in blue are the points (X, Y(X)) where X runs through the first 100000 primes. The red line is a line of slope 1 for comparison purposes (the Y-intercept was simply chosen so that the line went through the data points). The data was computed and plotted using Sage. |
| Date | |
| Source | Own work |
| Author | RobHar |
| Other versions | File:BSD data plot for elliptic curve 800h1.png |
Licensing
I, the copyright holder of this work, hereby publish it under the following licenses:
This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license.
- You are free:
- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
- Under the following conditions:
- attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.
|
Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License. |
You may select the license of your choice.
File history
Click on a date/time to view the file as it appeared at that time.
| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 00:36, 27 March 2011 | | 436 × 296 (5.07 MB) | RobHar | Optimize file: remove unnecessary and redundant commands to reduce file size from 19 MB to 5MB. |
| 03:31, 26 March 2011 |  | 436 × 296 (18.23 MB) | RobHar | {{Information |Description ={{en|1=A plot of the type of data used by Birch and Swinnerton-Dyer to support their conjecture. The curve in question is ''y''<sup>2</sup> = ''x''<sup>3</sup> -5''x'' (curve 800h1 of the Cremona database). Th |
File usage
The following pages on the English Wikipedia use this file (pages on other projects are not listed):
Global file usage
The following other wikis use this file:
- Usage on az.wikipedia.org
- Usage on be.wikipedia.org
- Usage on de.wikipedia.org
- Usage on es.wikipedia.org
- Usage on ja.wikipedia.org
- Usage on nl.wikipedia.org
- Usage on ru.wikipedia.org
- Usage on sv.wikipedia.org
- Usage on uk.wikipedia.org
