NAME¶

sympow - SYMPOW program

SYNOPSIS¶

sympow [options]

DESCRIPTION¶

Mathematical package to compute special values of SYMmetric POWer elliptic curve L-functions (up to about 64 digits of precision).

OPTIONS¶

-bound #

an upper BOUND for how many ap to compute

-info [] []

only report local information for primes/sympows 1st argument is prime range, 2nd is sympow range

-local

only report local information (bad primes)

-curve []

input a curve in [a1,a2,a3,a4,a6] form

-label []

get a label to the given curve

-quiet

turn off some messages

-terse

turn on some messages: default

-verbose

turn on extra messages

-rootno #

compute the root number of the #th symmetric power

-moddeg

compute the modular degree

-analrank

compute the analytic rank

-sloppy []

for use with -analrank; have X sloppy digits

-nocm

abort if curve has complex multiplication

-noqt

ignore even powers of non-minimal quad twists

-noqdcheck

don't check if quad-double stuff works

-mdspeed []

speed for moddeg; 2.0 is default, 0.0 is proof

-hecke

compute Hecke symmetric powers for a CM curve

-maxtable

set the max size of factor tables: 2^27 default

-sp []

argument to specify which powers this is a comma separated list in each entry, the 1st datum is the sympow then could come b which turns Bloch-Kato on then could come w# which specifies how many tests then could come s# which says # sloppy digits then must come p# which specifices the precision or P# which says ignore BOUND for this power then must come d# which says the derivative bound or D# which says do only this derivative (neither need be indicated for even powers) default is 2w3s1p32,3bp16d1,4p8

-new_data []

will compute inverse Mellin transform mesh for the given data: the format is [sp]d[dv]{h,c} sp is the symmetric power, dv is the derivative, h indicates Hecke powers, and c indicates CM case d[dv] is given only for odd or Hecke powers Examples: 1d3 2 2d1h 3d2 4 4c 5d0 6 7d0h 11d1 12c NOTE: new_data runs a shell script that uses GP

-dump-endiantuple

display the endian-tuple, used as a component in the binary data paths, and exit

-dump-versiontuple display the version-tuple (Major.minor.micro) and exit

-version

print program version and exit

-help

display this help and exit

Other options are used internally/recursively by -new_data

AUTHOR¶

Mark Watkins

COPYRIGHT¶

Copyright © 2005-2018 by Mark Watkins

SEE ALSO¶

gp(1)