curve #3549

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y² + xy = x³ − 355759649701494098454278593344226445800x + 2571650703088294583277645377334967427199821617554097640000

a-invariants: [1, 0, 0, -355759649701494098454278593344226445800, 2571650703088294583277645377334967427199821617554097640000]
rank (lower bound): ≥ 26
torsion subgroup: trivial
conductor (N): 63792228428829822214493508081106847405298069267762266519218947412602755537722789665933530960556330
discriminant (Δ): 24725122569031581112446176359584037803128078968680970096604760463894811319393037209344477970618789758324223744000000 ★ record for rank ≥ 26
Faltings height: 20.9893 ★ record for rank ≥ 26
naive height: 277.9156 ★ record for rank ≥ 26
primes of bad reduction: 2, 3, 5, 11, 17, 47, 139, 311, 233016733, 11306571687628397, 45197660685141016214255036668127757727696286467000519607586173
regulator: 4222850741397007374770432324810420.89088707682736776365193160178167421245802402465454421146
submitted by: Matej Jurasić
submitted at: 2026-09-28 08:35:18 UTC
last updated: 2026-09-28 08:35:18 UTC

Witness: 26 independent points log in to add more points →

(9426823042932189200, -7462037278044547857702965800)
(157881124509078244000/9, 1122747887022188011663953013400/27)
(10045532041503125000, -3402593837463785436658079200)
(-3335566698582335200, -61001632852676656764143329000)
(10214687312649126800, -1864384908278665163889485800)
(388861984573644996800/49, 5403300961935370153506834530600/343)
(13081724086029504640, 12505848881560487975014931560)
(-21354035320636975600, 20765963523222820102562034200)
(8304984758120662328300/841, -113041659709373394446895797994500/24389)
(5891534285144820230, -26080197910959935484961888330)
(9918750980219713850, -4333835337988241885615116300)
(1482914210223279320540/121, 9632989936427829686234937600760/1331)
(11547167560172307920, -1816591907924679032625975400)
(9919492582056940640, 4328647938936529575816615560)
(11641094007397586840, 2786187809787525936514179800)
(-18746426366801208880, 51505769137168817404441832600)
(77715061840956420560, -666553862465327324945558852200)
(7543468299464266409650564400/192626641, -589962881953575768306588960048718531821400/2673465150439)
(-334263850620261445848008145334/133868906161, -2874591568822540828214875352773878431551037548/48980089255092841)
(277501624507141234991670875570756240/42736692144731209, -204423514353396308803891130280320067266647425571650680/8834894270666596542123323)
(-3641830857122281082138181790541440/269310516526489, -309674550386597389712507716169064744949531920081080/4419569515282472081987)
(16984932340828637050618731027050/703013494681, -52981753479279340830053557388777527013610206500/589447991736736579)
(20363515310933469157368383694524320/12590348686398729, -63186408131882620385400548176625892225249356786835560/1412721767528156052455067)
(-186488147095818881891395526909680/9631159834921, 1402110503433439882534526245181153294824743302600/29889447374452015531)
(74212464543460173291930898821822337670540/6417464472378578230921, -1036016961097329617050588447066493261689909549435515888335800/514097165759890943260934978850469)
(701912749818069752848157420038311339350/53275363789704497401, -5091982208822109727891878671484399943203291388502711485300/388856744502150826573135124851)

Commentary

Specialization at T = -107/161 of a rank-17 fibration of X1008 (2-neighbour of the one in curve#751).

last edited by Matej Jurasić at 2026-09-28 08:35:18 UTC · history