curve #846

y² + xy = x³ − 890388688605835123536218905979825104833945491596640055500x + 10383942932786635402481776305650782666752061853846503229365337279722917845189552250000

a-invariants: [1, 0, 0, -890388688605835123536218905979825104833945491596640055500, 10383942932786635402481776305650782666752061853846503229365337279722917845189552250000]
rank (lower bound): ≥ 31
torsion subgroup: trivial
conductor (N): 6107775748197586381013294901509181537603643309915966469346075889066635203935238144975480962176195931608311285563333716551179539545352505603249739730
discriminant (Δ): -1403794172063572257365314952513606086951657668133997989185017750940266682739420265127042565243931713728180082619430038988504226669125044963116664840832866845474889472000000 ★ record for rank ≥ 31
Faltings height: 31.6366 ★ record for rank ≥ 31
naive height: 405.0380 ★ record for rank ≥ 31
primes of bad reduction: 2, 3, 5, 11, 17, 19, 37, 47, 1693, 19463013366014117941257134329894201607570211845394386921913562755517265337877130381987674995509634410847455827774124866179679010106183961
regulator: 184363041504338329516093612986246586634.3254599328959839139440648406066777240257224985383171252439193
submitted by: wgxli
submitted at: 2026-09-22 15:56:34 UTC
last updated: 2026-09-22 15:56:34 UTC

Witness: 31 independent points log in to add more points →

(246903839132700267388401700, 3188121327502976252139143196605062933291300)
(13735221956016104405303357700, 863419438176752476255018850716626096547800)
(14204911884288920776530111160, 776086588809006874326947032147663239914740)
(15606692452157860482383562700, 537796084708345829764729957721489621155300)
(16076783298623407312658506860, 473930325000169644749358625919749076165040)
(16087957805670676396343433100, 472578999453593319458162790925371890592400)
(16296061295293784603481077320, 449135415897484574850330133995494621848900)
(16568411683186986164870625400, 424085854719631496430158661059312324384500)
(17723940962630179680284595520, 412930047009402888263979581650058341846900)
(17996478501037614020510572300, 434349874342215936644201522079134805974500)
(18122883512480209908403040680, 446981540313852638736066211072794799324900)
(18212493410544071231825107000, 456876662638324809692674773179921159372500)
(18271753949455002106834343800, 463824012366257374286569788260827195424500)
(19252025532291819863674540840, 614603357423984877890516236360887281353060)
(20238538484311092098154369130, 808363150514794040503421186767760903782720)
(20282353822643527985937346960, 817554297359845332625147738159621036797940)
(20332342845982824776529564070, 828088207220924971417804985763806553479530)
(20588330122500116062946060056, 882776529757234040057811783525664691035252)
(7532291938414538664354033250, 2025986957543122490709466896149116893598750)
(-6094929823737951738016840460, 3947706171837435510458690137450613266925860)
(-7096526865082153033891718600, 4042922725843764217265650579818226813734100)
(12444459332239272339840307000, 1109388537402127269190354396556098206572500)
(34580845142558597889966569800, 4576737852018557251334833321521881051474500)
(-32515929227128769161036698920, 2226461999214643031039151068815247843398900)
(296344480861340216491234297000, 160535073089701490619497843844349961107862500)
(207412012485989609655327802762000, 2987107509234258206509163890577324199320159552500)
(6046131034045634958520968103000/49, 14467779933557731713359418423192314932570187500/343)
(-153683116569304359031524893746280/4489, 258811059320796439530022906518656944919303232700/300763)
(-1517602753169735672452174701399680/54289, 46355405876566991674405005574607099727696684765140/12649337)
(-8785220863216662674597365083088208/358801, 899237389388525394440521996088244363745469013283244/214921799)
(721348849592570893354406666356723600/22667121, 407776444486702851074776093633925824126775779719684500/107918163081)

Commentary

Specialization at T = 184419/28586 of the rank-17 fibration of X1152 given by: y^2 - (Lx+B)y = x(x+D)(x+E), where B = pq(L+p+q) - pE - qD, L = 317507T^2 + 50266T - 4769, p = 27228T^2 - 6004T - 130904, q = 6544T^2 - 435155T + 49011, D = 9278051832T^4 - 5997890895T^3 - 21678468935T^2 + 32553888590T - 11500771512, E = -51(201010368T^4 + 527976452T^3 - 260869191T^2 - 1427638947T + 39645998).

last edited by wgxli at 2026-10-04 18:07:20 UTC · history