SYMPOW(1) SYMPOW package SYMPOW(1)

# NAME

sympow - SYMPOW program

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: default
-terse
turn on some messages
-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

Mark Watkins