# sympow - Man Page

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 Ā© 2005-2018 by Mark Watkins