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sympow - Man Page

SYMPOW program


sympow [options]


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


-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


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


turn off some messages


turn on some messages: default


turn on extra messages

-rootno #

compute the root number of the #th symmetric power


compute the modular degree


compute the analytic rank

-sloppy []

for use with -analrank; have X sloppy digits


abort if curve has complex multiplication


ignore even powers of non-minimal quad twists


don't check if quad-double stuff works

-mdspeed []

speed for moddeg; 2.0 is default, 0.0 is proof


compute Hecke symmetric powers for a CM curve


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


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

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

print program version and exit


display this help and exit

Other options are used internally/recursively by -new_data


Mark Watkins

See Also



January 2024 SYMPOW (2.023.6) SYMPOW package