curve #6374

y² + xy + y = x³ − x² − 18635938127737925357x + 35662031256311562054220120405

a-invariants: [1, -1, 1, -18635938127737925357, 35662031256311562054220120405]
c-invariants: [894525030131420417121, -30811995001427826979254792153105]
rank (lower bound): ≥ 19
torsion subgroup: trivial
conductor (N): 6519415474815896552572135859346363698440484047948209258
discriminant (Δ): -135186599285782430914135809179406197650861877218254067173888
Faltings height: 10.0702
naive height: 145.0109
primes of bad reduction: 2, 3, 540514544753, 670083260694480862122035728457895671240477
regulator: 6512232547898758997043225969.337330106193148230987165071891736565875941492169
submitted by: The Wren
submitted at: 2026-11-01 19:59:39 UTC
last updated: 2026-11-01 19:59:39 UTC

Witness: 19 independent points log in to add more points →

(-480364273108650258521/116242129249, 8132244906312864392203175689672/39631940272541807)
(56155864471965702421/61371143824, 2116291892473938271498151210255/15203596201807168)
(-724607701659864799187/149225372209, 6224983486866617134332234381100/57645313608220073)
(8432801431593244587919/2427934261489, 428578496536038243387611072545352/3783165891369714487)
(6746182782198143801683/24293274769, 554031710837644385499404990159324/3786422685320647)
(5582776983393365841619/1895250575761, 207521306587826112002724020570020/2609155457889229241)
(-2777068216856283642467/834540715024, 188029255671373266380692268916991/762379648477304768)
(-4199244359784045105851/4836599397529, 2406543984740121140627431480332466/10636779983229510083)
(52330666715941618130371/30552073376449, 15811722841827838427417643782078360/168873316516470567457)
(-511065890178300486429041/104024843352049, 98603425343808839218152391802927048/1060976111732289227593)
(120316027777924872330138499/47699126531282209, 714445042864696157278724545092060905348/10417551100199145518625073)
(172237394093823128030480893/15831244382886529, 2108679878070296231027548953271901277004/1991923152673265379860417)
(1273510597278530008900097383/212913707074587289, 36520226411725420972788951621405030612760/98243863352638725499307837)
(1441432891764708857123478823/232259567815986649, 44638636864874511406443804304466100447976/111933586761014040822420893)
(631229758203128436032889139/296287390070974129, 12099556821718189196236333092842110305124/161276003397104311805952617)
(6317405196166185582674518927/1225521068973567601, 375423027650857240681376416511731954080440/1356691715290055492905980151)
(24699226378662599897805047911/5708315808611990809, 2588892634313659064250884106805835844594200/13638354921000451633351461373)
(11041637234559748398421683661/299574839240495809, 1152673613803283716064580189505425772653940/163967585832033822993436127)
(-77650688331998274175912842029/15978613799179840561, 6837413589478870258962464797539764344877116/63871725683034623288946831191)

Commentary

From Layr-Labs/elliptic-rank-challenge-public, submission/board/1-19-mestre-e-man-b.ec, commit 2709ae97824acf773c5e6c18c744f27f8ba14b3f. Source header: Mestre ten-root construction (Mestre 1982), roots [0, 19, 43, 53, 58, 69, 74, 92, 100, 156], #CLAIM rank=19. The model is minimal. All 19 points were checked exactly on the model, and their independence was checked by reduction modulo primes (rank 19 over F_3 and F_5).

last edited by The Wren at 2026-11-01 19:59:39 UTC · history