curve #3830

y² + xy = x³ − 182645089820280547924136483834076781834824950x + 946748874116068735303139059854484216276432371813766534557615502500

a-invariants: [1, 0, 0, -182645089820280547924136483834076781834824950, 946748874116068735303139059854484216276432371813766534557615502500]
rank (lower bound): ≥ 25
torsion subgroup: trivial
conductor (N): 90797695234002305494508179145896944871582886422866863062310751430059652629718524608948243799990
discriminant (Δ): 2729516170706406998644022764007003870311537155165602364299291010584701664209732025301844028533791674833699617343273879291720128000000
Faltings height: 24.2683
naive height: 317.3620
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 67, 73, 139, 2281, 70925927, 25402820748429333857009, 717576790813508381092604275527944678370494477
regulator: 33386201951032979605427584.05823219089308142322092449207186587750376677690787838419041434
submitted by: 7fff-zip
submitted at: 2026-10-03 05:22:17 UTC
last updated: 2026-10-03 05:22:17 UTC

Witness: 25 independent points log in to add more points →

(-2719341682879857489800, -1193027342510844021539045070767750)
(9103569828855011178400, 196175292960702267381193529921050)
(8724339994530862149130, -131667656368863335709770687571080)
(6777442781382410578900, -142110730800775421460226145187950)
(-7709766122924230953152900/4489, 336985042494462802693706643679649599150/300763)
(136605030206321312128900, -50251109455894865176199145699990950)
(-15065184722155508732060, 528336747986684546843041614281410)
(-13065298068154075109180, 1050137478938622318982727946772450)
(31237250499446803404940, -5071652567026892203428683426115590)
(15755870229892749995770, -1407256584965742751665763537553720)
(8456129663364979335900, -83327125144787009615715468466950)
(-11565048048334683512000, -1229723158754895372426133856680550)
(-2817751889754696045420, -1199593782902557915799803398186030)
(15248143031098439736460, 1306534775408995382487615997328890)
(267744372009992821946284/25, 58505411786316805849653128590922642/125)
(14247255567434649628600, -1111992209631164506223817809154950)
(7372189928160208262206, -30448183644947695527072555854018)
(10158239683038763134550, -373662061112943088851775416490850)
(8336278458165099883900, 59042650716940281459430054199050)
(7269641166908039037850, -56287653397588314044781248845400)
(11096856467599384468900, -535193341724333298156162262470950)
(5413600121762774705950, 341523251326701111697945336286500)
(5243666896541349000820, -364964314378063959405646374577550)
(7408250894210578784740, -15785845229192887305093661139390)
(9458699193765261040150, -255744522162282004948561674020450)

Commentary

X1008; T=477/1201; 2-neighbor step: yes (Q has vector q=[1,0,0,1,1,0,1,1,0,-1,1,0,0,1,0,1,-1] in source section basis; h(Q)=12; F'=O+Q-F).

last edited by 7fff-zip at 2026-10-03 05:22:17 UTC · history