curve #5538

y² = x³ + x² − 174415675289207070153335839785042753312373062175018745x + 26860964405576720597086181981420751279246537771729234545135321882240740836861975

a-invariants: [0, 1, 0, -174415675289207070153335839785042753312373062175018745, 26860964405576720597086181981420751279246537771729234545135321882240740836861975]
c-invariants: [8371952413881939367360120309682052158993906984400899776, -23207873246418286595882461282179243588560644838934780505089231060219441989454145024]
rank (lower bound): ≥ 30
torsion subgroup: trivial
conductor (N): 523403742197855573452550875151551119972646967474610428100497127214231002949124080448815961527234973954806632963204553406947581242467793280
discriminant (Δ): 27882701559717624181016032249031885510793171772137168989334771637500435342274941149583328083414101875995971514086643324666451355425190623495879933669265280000000
Faltings height: 29.5471
naive height: 379.3934
primes of bad reduction: 2, 3, 5, 23, 37, 43, 53, 191, 953, 13093, 70589, 885128202690681017, 41041689398920602713011956863549610739147989478933358376451012958954877059608600522261376392561
regulator: 2972436210709680397115382831605036197.3723966344080197949690919565784290519234827312949952110528386
submitted by: Matej Jurasić
submitted at: 2026-10-22 23:50:55 UTC
last updated: 2026-10-22 23:50:55 UTC

Witness: 30 independent points log in to add more points →

(141234568113675745278638335, -2246035722590237325798640058034191084700)
(355208551820617637568269035, -3118460282077684981890535974703967818500)
(465882488010923197536713035, -6835343126477959726211996991794248105500)
(298176301361991318461899285, -1168303059859788937349348851481859964500)
(175839280464942901016128315, 1276202119750683279259287990962870136180)
(299509024080310466024693035, -1220470831419908409006846161236085389500)
(-131119161639357564065652245, 6890280846633672657031762950757756532220)
(351360351777919703116073410, 2992505014361567028727941923106002201625)
(291518679165795441503597935, -888656250652346442496124193095643866100)
(-39286401623961448844409365, 5801076900315261242346359103624745872900)
(-477338697497879362894216715, 1163455183886315813112890604469389205500)
(-115510038887054601553901400365/361, 48456611089225372209464500582431740256289500/6859)
(1410708705541818132110522410, 50874957594930293442582660641922118696125)
(-471885517519370735317509830, 2021792185382848034461794974205962058165)
(141893067225679045513463035, -2229218149731752717445495841795264855500)
(-429825079068256726239869630, -4734890178571716494950850076918679845465)
(3117270906730940092270827865/16, 33567493433581881558113636220858267798555/64)
(9726951710564875535735456511415/169, -30335680179988557661290861462586381490369956500/2197)
(98904721176585155059656257785/256, -16959405506299097670980916324063803118162675/4096)
(132600273716459438864235343, 2462699034776478499783284842751523624236)
(-49597612730654596113166567085/169, -15959832254572176356758902555470453992198500/2197)
(2915431447947385424847200779, -155880642972260459621965701757944377898660)
(95351499590242085762046720835/3481, 965585510808893398262992318812281690642446500/205379)
(1116182535899066525364732442183/3721, 281057597136484612003868202084334076127503964/226981)
(-45385353729576494199068845475/169, 16194231234717061512247012651651878393178020/2197)
(33818388838064083329511292608777/113569, -44110698829203936157549718721717472073212776912/38272753)
(-11415935853458186963870577089510/134689, 316647621149107785269785147980335133054474559125/49430863)
(2267757956816246462117198211555025/1142761, 105763966876650537245226897187826761152772687769760/1221611509)
(233050436772952940942813589574885/96721, -3507363797537229736009073470727044181062087334100/30080231)
(-801734959493893152719153630079408857/3985523161, -1845633257958110790921488476567709056434664912846966356/251610062677091)

Commentary

Specialization at T = 21951/6607 of a rank-16 fibration of X1152 (two neighbour steps from the one in curve#3856).

last edited by Matej Jurasić at 2026-10-22 23:50:55 UTC · history