curve #6451

y² = x³ − 422058643576044150573156977298567x + 2761525235925156574202779021667844461279015062890

a-invariants: [0, 0, 0, -422058643576044150573156977298567, 2761525235925156574202779021667844461279015062890]
c-invariants: [20258814891650119227511534910331216, -2385957803839335280111201074721017614545069014336960]
rank (lower bound): ≥ 24
torsion subgroup: trivial
conductor (N): 1047158144325370182612894252450740657656290273227777836363942835433327768750695723703750813144
discriminant (Δ): 1517256755741069967952935643414946759616613353007377684887134964658740737320408053554628258187109632 ★ record for rank ≥ 24
Faltings height: 17.7497 ★ record for rank ≥ 24
naive height: 236.9817 ★ record for rank ≥ 24
primes of bad reduction: 2, 3, 13, 43, 26017644214007408631805164292654061261585427182165022767937359258430922499271907267535053
regulator: 110748773873548810370854656.49270501167317348998549440434322090808113416838142505676729
submitted by: apkorte
submitted at: 2026-11-03 16:25:05 UTC
last updated: 2026-11-03 16:25:05 UTC

Witness: 24 independent points log in to add more points →

(7563601615836489, 44055006204596375144286)
(661203807786693, 1575673673604554760860754)
(7137147111837927, -335840450097445429766292)
(5973740863427521, -673374098801031913103338)
(-11836181373011955, 2469594262017806445137850)
(-9996855817755363, 2445757060813744271709258)
(1011680963646108969/25, 900963216098583116938849422/125)
(44317656328158345, -8432032664694400965767070)
(2287157310012556434/25, -3377003065277948418968146998/125)
(116250535091528001/4, -31027993556039183634682167/8)
(723194367495623769/100, 295734427458198758057087397/1000)
(16448846264368713, -519251454157676268618846)
(19985319187579293, -1519521135650110831511754)
(-22058842461489039, 1156711885272421035437178)
(20070170334189666, -1541180244949477800978258)
(-22243962660007923, 1069394907445988690597958)
(15966700055618119, -305156190165770899665476)
(59467007186259003, 13709763735555784231468404)
(17344725650256513, 811795900311340278309846)
(31254522793074843, -4483426608455888018696004)
(7376806144052871, -222499627663736307889188)
(144192405231294201, -54220595889045097909303218)
(13382019934634909449/225, -46281282713412773952472954082/3375)
(11039931726264065838/529, -21223430286274062226825638336/12167)

Commentary

From the Layr-Labs elliptic-rank-challenge-public repository (https://github.com/Layr-Labs/elliptic-rank-challenge-public), file submission/board/1-24-a.ec in branch submissions/5371b03c-5214-4417-9855-76b73cc8d56d; pull request #73, 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 2026-11-03 16:25:06 UTC · history