SYMPOW(1)

🌸 NAME 🌸

okay bestie, this is the manual page for sympow, and the manual name is SYMPOW(1). The NAME section is literally sympow — SYMPOW program. That's it, that's the name, and we're already iconic. 💅

✨ SYNOPSIS ✨

sympow [options]

that's the whole synopsis — sympow plus [options], no cap. 🦋

🦋 DESCRIPTION 🦋

okay so sympow is a mathematical package to compute special values of SYMmetric POWer elliptic curve L-functions, up to about 64 digits of precision. It's giving serious number theory, and the DESCRIPTION is short but powerful. ✨

👑 OPTIONS 👑

okay, here come the flags, bestie. One bullet each, no skipping, because we keep every detail. 🫶

• -bound # — an upper BOUND for how many ap to compute.
• -info [] [] — only report local information for primes/sympows; the 1st argument is prime range, the 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; this is the 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. It's 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 specifies 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. That's the whole options list, and yes, it ate. 💅

💌 AUTHOR 💌

The author is Mark Watkins, periodt. 💖

©️ COPYRIGHT ©️

The copyright is Copyright © 2005-2018 by Mark Watkins, preserved exactly. 🎀

🔗 SEE ALSO 🔗

gp(1) — that's the see-also, bestie. Go check it out. 🦋

---

okay that's the whole page, mwah 💖 — this one's from the SYMPOW package, version 2.023.7, dated September 2024, and it's the SYMPOW(1) manual page. bye bestie 🎀