curve #441

y² + xy = x³ − 1009193317631438952446667509552594424471980395090x + 393673064651019213659149270108184935843722977273821305373879015181970692

a-invariants: [1, 0, 0, -1009193317631438952446667509552594424471980395090, 393673064651019213659149270108184935843722977273821305373879015181970692]
rank (lower bound): ≥ 23
torsion subgroup: trivial
conductor (N): 63493486231759073250764792331195308001819432109256292041160102370676017991187846658493352760077810367295827043493210
discriminant (Δ): -1169310157450746998470504412569198371840807035010713758970313250668877020355620249144096471742468140740182835263369822877570113800810504192000000
Faltings height: 26.4619
naive height: 343.2309
primes of bad reduction: 2, 3, 5, 11, 13, 17, 37, 109, 126684609041, 641974397962149517, 148822892203408848910326967, 482038481167953216413710853704979534567086915783643
regulator: 3289087604604765304000906511.31384066048365214210977443359711301715393124170499651128
submitted by: Nikita-Shulga
submitted at: 2026-08-30 13:52:25 UTC
last updated: 2026-09-02 17:35:49 UTC

Witness: 23 independent points log in to add more points →

(422682328103356152796604, -206449646484424763421301367876342722)
(584032144659128830151324, 59002730241606557565068408965084838)
(33541155694824338433746518/9, -187827802973374257240611503207264395080/27)
(95933234077266270906500408/169, 133931736204493543460659895507694905330/2197)
(322779831970338884152574, 318677296633676389024528334023776338)
(-1139193843462111118760626, 254826803880159039477384411438963488)
(-1158881430335550915498676, 82604777855456168423565002225734838)
(373926627609847224541444, 261900079635668458776763123733579998)
(-1149101815153807689745756, -189801748265881382692902478009012642)
(-86954792342827495188676, 693375643512548049995051816471563838)
(304664277755500501081124, -338359199409686615033559934632133762)
(-885388928584885311220636, 770151460716105267626725316662096958)
(-763682073912116367970036, 847931985102419816906808511375809278)
(3613831696871963130019871/4, 3746737858037457960760751929651588729/8)
(526317401245983483597524, -91171526734921989853155160839432562)
(-926382017343444924031226, 730455825186188772763248594364681288)
(665499935275079642710724, 129608458304492359032365906007526238)
(-376320509666052892566316, 848622283034081571628435566484550798)
(47608300942607969173601556164/78961, -1468501618677628751958151997157398575488242/22188041)
(535232153980490071069508, -82765680124139127984434826040657954)
(528052816369827856378724, 89486426397767969861513864370207038)
(2215456284282325235532262, 3005304484682756187979409098153656370)
(31819516750296785477500292/49, 37827268228094169316655632342884214898/343)

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