MWRANK(1)

💖 MWRANK(1) 💖

okay so bestie, welcome to mwrank — she lives in the User Commands part of the manual (section 1, if you're keeping score) and she's about to tell you everything about your elliptic curve. Buckle up. 🎀

✨ NAME ✨

mwrank — determines the rank of an elliptic curve E over Q by 2-descent and generating points for E(Q) modulo torsion. No cap. She does the math and she does it well. 💅

🌸 DESCRIPTION 🌸

Okay so the whole vibe of mwrank is: it's a loop 🌀. You type in a curve, she looks at it, she tells you everything she can compute about it, and then she's like "next?" and you give her another one. It's giving conversation. It's giving main character energy. 🫶

To enter an elliptic curve, you hand her its Weierstrass coefficients — and those can be integers or rationals, whichever, she's not picky — and you can give them to her in either of these two formats, iykyk:

• as a bracketed list: [a1,a2,a3,a4,a6]
• or just spaced out: a1 a2 a3 a4 a6

Both slay. Use whichever feels right in your heart. 💖

🦋 Command line options, bestie 🦋

Here's the whole lineup of mwrank command line options. And the best part? They can be in any order. Go feral. 🌈

• -h — help — prints all this info and then quits. She said bye. 👋
• -q — quiet — turns OFF the banner display. For when you want her to be lowkey. 🙈
• -v n — verbosity — sets verbosity to n (default=1). Turn it up or down, your call. 🔊
• -o — PARI/GP output — turns ON extra PARI/GP short output (default is OFF). ✨
• -p n — precision — sets precision to n decimals (default=15). Numbers get more detailed, the way that… yes. 🔥
• -b n — quartic bound — bound on quartic point search (default=10). 🎀
• -x n — n aux — number of aux primes used for sieving (default=6). ⭐
• -l — list — turns ON listing of points (default ON unless v=0, so heads up that this one's already on unless you've silenced her). 👑
• -t — trace — turns ON trace of quartic equivalence testing. 🚨 debugging only, bestie — this is not for the casual scroll. 💀
• -s — selmer_only — if set, computes Selmer rank only (default: not set). 🧚
• -d — skip_2nd_descent — if set, skips the second descent for curves with 2-torsion (default: not set). 🍓
• -S n — sat_bd — upper bound on saturation primes (default=1000, and -1 for automatic). 💜

lowkey important: -t is debugging only, so don't come for me if you turn it on and get a wall of trace output. That's literally what it's for. 😭

and that's the whole page, bestie!! she ate and left no crumbs. 💅

this was mwrank 2012-07-30, from May 2012 — go forth and rank some curves, you gorgeous genius. 🦋✨🎀💖