curve #639

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y² + y = x³ + 905190726253138078813130388631347

a-invariants: [0, 0, 1, 0, 905190726253138078813130388631347]
c-invariants: [0, -782084787482711300094544655777484024]
rank (lower bound): ≥ 14
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 20010625156114155541673742142742291061353130759380219529827363403
discriminant (Δ): -353967948386503297376666824762968386584275530002676703263116231235667
Faltings height: 11.8322
naive height: 165.2945
primes of bad reduction: 3, 7, 19, 17431, 11742876743532235184470771
regulator: 732519227902125394883.687598436574062267928323311493106138004618773
submitted by: Maksym Voznyy
submitted at: 2026-09-08 07:50:13 UTC
last updated: 2026-09-08 07:50:13 UTC

Witness: 14 independent points log in to add more points →

(130532552506642607655138651/233987042323225, -1495228199014824513506320978097622485649/3579214381147924847875)
(-6761867142250979095420727/226852939243044, 101283533946021256276317004871748041383/3416776850114722746072)
(77180100803647145445/1055665081, -1234774404217760375543993286507/34299614146771)
(1835726614564923927397411791/13742756842545025, -92388453458951421743266312055502484290911/1611056581986916220962625)
(-1704666330297626261969487/25552650931369, 3185734105853986979757327010010630785/129167705009985834347)
(1027738585930569401993226325/989883054233649, -32960937222034435093811573541735511506512/31144103534702137933143)
(-62341122194757047149214723415/1140447308379260176, -33171910194980957335054373521791790557621067/1217903382985911502049200576)
(424766638316061632380087683/2676765491576089, -9695364613039580296873890177761364518698/138489066287156682626563)
(8594075767099410695103237633/186216136880071684, -2545553698282027686439800034537918702603077/80357417153987498270069752)
(-27672814120711636048941/756682515625, -19260964326839416608815673264691002/658219203279296875)
(843290670894618195564141064065/15085522385401034116, 1925426890049955793777908183952902296800121651/58592297865771922143781555336)
(5729420131301227968451593/181274260498969, 74699789195188741576996424755498839588/2440642745071405308797)
(286430197110849008889690747/1636771195506841, -5241048514132610978502515523508690859535/66218899722984936035389)
(174323827708721443585/65415744, 2301683033092161536478600423551/529082537472)

Commentary

Reynya - Voznyy (2026)

last edited by Maksym Voznyy at 2026-10-20 22:23:39 UTC · history