Module: sage.databases.stein_watkins
The Stein-Watkins table of elliptic curves.
SAGE gives access to the Stein-Watkins table of elliptic curves, via an optional package that you must install. This is a huge database of elliptic curves. You can download the database as a 2.6GB SAGE package from http://modular.ucsd.edu/sagedb/, which you install with the command
sage -i stein-watkins-ecdb.spkg
sage -i stein-watkins-ecdb-mini
This database covers a wide range of conductors, but unlike CremonaDatabase(), this database need not list all curves of a given conductor. It lists the curves whose coefficients aren't ``too large'' (see [Stein-Watkins, Ants 5]).
SteinWatkinsAllData(n)
returns an iterator over
the curves in the
SteinWatkinsPrimeData(n)
returns an iterator over
the curves in the We obtain the first table of elliptic curves.
sage: d = SteinWatkinsAllData(0) sage: d Stein-Watkins Database a.0 Iterator
We type d.next()
to get each isogeny
class of curves from d
:
sage: C = d.next() sage: C Stein-Watkins isogeny class of conductor 11 sage: d.next() Stein-Watkins isogeny class of conductor 14 sage: d.next() Stein-Watkins isogeny class of conductor 15
An isogeny class has a number of attributes that give data about the
isogeny class, such as the rank, equations of curves, conductor, leading
coefficient of
-function, etc.
sage: C.data ['11', '[11]', '0', '0.253842', '25', '+*1'] sage: C.curves [[[0, -1, 1, 0, 0], '(1)', '1', '5'], [[0, -1, 1, -10, -20], '(5)', '1', '5'], [[0, -1, 1, -7820, -263580], '(1)', '1', '1']] sage: C.conductor 11 sage: C.leading_coefficient '0.253842' sage: C.modular_degree '+*1' sage: C.rank 0 sage: C.isogeny_number '25'
If we were to continue typing d.next()
we would iterate over
all curves in the Stein-Watkins database up to conductor
.
We could also type
for C in d: ...
To access the data file starting at
do the following:
sage: d = SteinWatkinsAllData(1) sage: C = d.next() sage: C Stein-Watkins isogeny class of conductor 100002 sage: C.curves [[[1, 1, 0, 112, 0], '(8,1,2,1)', 'X', '2'], [[1, 1, 0, -448, -560], '[4,2,1,2]', 'X', '2']]
Next we access the prime-conductor data:
sage: d = SteinWatkinsPrimeData(0) sage: C = d.next() sage: C Stein-Watkins isogeny class of conductor 11
Each call d.next()
gives another elliptic curve of prime conductor:
sage: C = d.next() sage: C Stein-Watkins isogeny class of conductor 17 sage: C.curves [[[1, -1, 1, -1, 0], '[1]', '1', '4'], [[1, -1, 1, -6, -4], '[2]', '1', '2x'], [[1, -1, 1, -1, -14], '(4)', '1', '4'], [[1, -1, 1, -91, -310], '[1]', '1', '2']] sage: C = d.next() sage: C Stein-Watkins isogeny class of conductor 19
Module-level Functions
[max_level=200000]) |
Class: SteinWatkinsAllData
self, num) |
Functions: iter_levels,
next
self) |
Iterate through the curve classes, but grouped into lists by level.
Special Functions: __getitem__,
__getslice__,
__init__,
__iter__,
__repr__
self, N) |
Return the curves of conductor N in this table. (Very slow!)
self, min_level, max_level) |
Return all data about curves between the given levels in this database file.
Class: SteinWatkinsIsogenyClass
self, conductor) |
Special Functions: __init__,
__iter__,
__len__,
__repr__
Class: SteinWatkinsPrimeData
self, num) |
Special Functions: __init__,
__repr__
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