curve #400

y² + xy = x³ − 2847874483810983397135985687546115504035875512904930x + 58635720945607333252276967459894829928661530156981574300268557162161405688900

a-invariants: [1, 0, 0, -2847874483810983397135985687546115504035875512904930, 58635720945607333252276967459894829928661530156981574300268557162161405688900]
rank (lower bound): ≥ 28
torsion subgroup: trivial
conductor (N): 162476637634535294286778649145036191011122479825714081504632862793032411365136143677415696261543655627501450769615910710 ★ record for rank ≥ 28
naive height: 367.0536 ★ record for rank ≥ 28
Faltings height: 28.3938 ★ record for rank ≥ 28
discriminant (Δ): -7048150461482958989059028240663305327955857359757275013969839824285806183042275878060026843545994391532837981874324443836036952899392928175564470784000000 ★ record for rank ≥ 28
primes of bad reduction: 2, 3, 5, 7, 13, 17, 19, 41, 43, 61, 953, 11933313623798286182113727713229900381, 7929321922016405507363418365097646209609868260547815576055693906829
regulator: 32379867911385311617065075405354.36525158606434013865414461823320237438445947474009583326618687
submitted by: NDElkies
submitted at: 2026-08-28 16:44:48 UTC
last updated: 2026-08-28 17:26:19 UTC

Witness: 28 independent points

(-56316432438418421992818940, 201017417373219270221316816759255341870)
(31310681013828987227734160, 12748779416247698893684682310638069870)
(-14952798109836831794409340, 312851680935856045315724246698679019470)
(31430424930451944642804260, 13230279324386196106791476952834185870)
(42158185422310724020569380, 116201439155552815018159461639184385870)
(26176046115444986872815860, 45000794424846253428181895049992438270)
(19272274789979674530444260, 104445300140638540022906629275354689870)
(37102231413803185419260900, 63617987902793758632525763064220430670)
(22802372004142985022617060, 74521668777620213417029576363857521870)
(28766156129648150573342180, 22739293120787095427343503873720175950)
(31245855580796449611679180, 12525334098413056083097766098104421870)
(71805096146868607306742660, 473675915575284998050290344124961949870)
(27428006265451832651333060, 34031870468449004266810814474909065070)
(33960900398379483822997160, 32983294424038486232060249539670355470)
(-61488043852635609467652700, 35682126276638344742650007644751374670)
(33375495052728396484194980, 27645146736345952283980286126032547150)
(-43060058255238702995164510, 318472531722065647737269666613927757340)
(50339254610204432846182820, 206972352944327838326347908362183552270)
(59262410408224261129413860, 313042125822851566276790733754710200270)
(26089850386442226416589860, 45759684809426758046246293439610344270)
(193657777985259537485039660, 2601909912846231423300959232223121984870)
(5701651529225412201636260, 206357667803119013430724895774175041870)
(22954480426330066068031460, 73206182544706725037978323776064833870)
(31775891714105641329702890, 15043914947597990779833417058412702690)
(2388938788572327423354260, 227697072594448148106171821457867785870)
(29459540528613265640091860, 17479628427422664117698378231846675870)
(31247695763251676960491760, 12531298125468199348888572492547685870)
(-23722075773181133972912860, 335922503502457806842314568917948642190)

Commentary

Noam D. Elkies and Zev Klagsbrun, January 2026

last edited by NDElkies at 2026-08-28 20:42:46 UTC · history