curve #6417

y² + xy = x³ − x² − 145601943705174486014x + 745592900635242913542755158744

a-invariants: [1, -1, 0, -145601943705174486014, 745592900635242913542755158744]
c-invariants: [6988893297848375328681, -644192266117399857460622768175765]
rank (lower bound): ≥ 20
torsion subgroup: trivial
conductor (N): 21300281185296056865193415720121521294395818191599774348391114
discriminant (Δ): -42600562370592113730386831440243042588791636383199548696782228 ★ record for rank ≥ 20
Faltings height: 10.5599 ★ record for rank ≥ 20
naive height: 151.0911 ★ record for rank ≥ 20
primes of bad reduction: 2, 35702148542950426697, 298305312909549069775155765411664081592381
regulator: 53163368044724499693.4523649968425718414804516422820135110299622506556968283313
submitted by: apkorte
submitted at: 2026-11-02 14:15:20 UTC
last updated: 2026-11-02 14:15:20 UTC

Witness: 20 independent points log in to add more points →

(6192856206, 285314492349940)
(6120056146, 289354965550720)
(7568205420, -277739508362468)
(5754596508, 313490534908432)
(5450094490, -337546195441442)
(3634146174, -514249218059612)
(2150854476, -665113500100756)
(233803356, -843542325795596)
(13895824972, -1185558941919800)
(-686807151, -919384987699607)
(-8262874953, -1176658488035275)
(17101325499, -1804719199339747)
(-10346349819, 1069816514179265)
(25643102598, 3724770291173932)
(29714679391, 4759818717368860)
(7019595207/4, -5631238404316669/8)
(-17547454041/4, -9121054130580053/8)
(96692603868, -29844487685098768)
(63643302997/9, -7122513371332586/27)
(-1590713680245/121, -828716666947004873/1331)

Commentary

From the Layr-Labs elliptic-rank-challenge-public repository (https://github.com/Layr-Labs/elliptic-rank-challenge-public, file submission/board/1-20-m10-125404.ec), where it is recorded as a find of that challenge; not our discovery. Posted by apkorte with Claude (Anthropic), which moved the points to the minimal model and checked their independence.

last edited by apkorte at 2026-11-02 14:15:21 UTC · history