curve #3820

y² + xy = x³ − x² − 831658772438163886278513352623019822849519x + 309254261648699321181693416732495360351211792091765489658696089

a-invariants: [1, -1, 0, -831658772438163886278513352623019822849519, 309254261648699321181693416732495360351211792091765489658696089]
rank (lower bound): ≥ 27
torsion subgroup: trivial
conductor (N): 161733719932330532848018621509076390882231700237713239088433471953106706713142338296337888380611807172138406
discriminant (Δ): -4501491071126521672826088123255421817807162633167296588962409887358163309807033432877792639397273150588847215392360568114940988
Faltings height: 23.0528
naive height: 301.3017
primes of bad reduction: 2, 7, 11, 13, 19, 23, 47, 103, 337, 28661, 27969135920189, 7533601172584212751, 1443356844639649258739664944850741534630719573571510766541
regulator: 334084029967574492802484320787.41766124348296256630349085842628734625299673787966999538125358
submitted by: 7fff-zip
submitted at: 2026-10-03 05:01:19 UTC
last updated: 2026-10-03 05:01:19 UTC

Witness: 27 independent points log in to add more points →

(2942859095922542447960, 152801159826794122610632993658677)
(2617352406820895306341/9, 258960124607654251297667259361586/27)
(1872024238109643720740, -72889166219504848863095309730297)
(446804660385180053265, -5182936291135941382693397941847)
(-477000387090353592157, 24442263005241416229306417795135)
(-804663220499221426398, -21388169944009732465107079591217)
(465066382417166391027, -4802646844148008118802354285410)
(6879401927395400927833, 565830089739445852097179817538470)
(574942499954528014618, 4598982034846509540266648501235)
(55620745435925885432452/81, -5738217902663413908475966447967923/729)
(3633627976818684089125, -212751081142334877268272343009467)
(-944889108561776994307, 15857742727129848006068547992397)
(559765503284864610042, 4372167447578854747633924331563)
(-125319867340240003430, -20285696229067056521848447404957)
(-1057925781870162742228, 2247136078863323401991671693605)
(-48549631885536296994496/49, 4346637025134746556278118306323917/343)
(-768601983448082251159, 22235511770743304970213268671025)
(15928648539320474266, 17204973199737902588649210099875)
(202092229695522625768, 12224409562652089832219368229397)
(541354477300276647316, 4205226854091831216156423278709)
(444582688341620391872, -5233221933989692923642303964677)
(565736728731241594693, -4452296080991294906118678592603)
(2665250250489913178327/4, 57094438010785188783792827434395/8)
(570592286198346084674, 4526265876199390422115696668103)
(797298179745520341274, -12369488316467774920486838319117)
(1485443509973057457131, -48492950569355251480812804628770)
(2082047164064698996474, -87196388599009171245380487052837)

Commentary

X1008 at T=8853/151

last edited by 7fff-zip at 2026-10-03 05:01:19 UTC · history