curve #245

y² + xy + y = x³ − x² − 25880411472355347134118026792x + 1606663697747901005185875883284420820193259

a-invariants: [1, -1, 1, -25880411472355347134118026792, 1606663697747901005185875883284420820193259]
rank (lower bound): ≥ 20
conductor (N): 272066437942638823321634957004224153562929337633497250319389959310 ★ record for rank ≥ 20
naive height: 207.8886 ★ record for rank ≥ 20
Faltings height: 15.1332 ★ record for rank ≥ 20
discriminant (Δ): -5737429639444055753512327119829925015713334222025694979826677816527336990079139840000 ★ record for rank ≥ 20
primes of bad reduction: 2, 3, 5, 13, 19, 37, 7770053, 763973980372286963203, 55722582408764114465841769948159
regulator: 4687798591445119467.32292703579184309810358227475172994834982074863674547612846
submitted by: David Renshaw
last updated: 2026-07-07 01:04:58

Witness: 20 independent points

(45492869957717, 723492619381097668641)
(103561597049417, 192731719560345258741)
(111830641498667, 333174093470012383491)
(316677539205677, 5016853361860584594681)
(92008168616117, 65953506306453213441)
(147881370863967, -1006695588776782646359)
(213774572035037, 2417332168050319812441)
(81536578719167, 196306066193578043241)
(294423088161917, -4416891036870168333159)
(227707758469997, -2742321749648483486439)
(94836710011277, -72195187870086062919)
(132211123753677, 704277531895181059641)
(91603447091117, -67755953909555099559)
(60334338604917, 514603898948192002241)
(82129229001677, -187361656905064421319)
(20079468981897, -1046467649553400314559)
(107362804572947, 256157490251353593441)
(305606512192501/9, -23646417837002335990141/27)
(1413476686249589, -52811301360597927383607)
(3892455620987453/49, 78262410657484049671263/343)

Commentary

Rank-20 at naive height 207.89: Mestre-family specialization T=5801/160 found by wide-denominator vectorized sieve (n>20 window), certified via famcert3 with base-point injection.

last edited by David Renshaw at 2026-07-07 01:03:48 · history