curve #363

y² + xy + y = x³ − 77784861105517331567918462464043246062399071551x + 9729372994024391552036598189578155261901018816064506695929640000090598

a-invariants: [1, 0, 1, -77784861105517331567918462464043246062399071551, 9729372994024391552036598189578155261901018816064506695929640000090598]
rank (lower bound): ≥ 27
torsion subgroup: trivial
conductor (N): 14445543932749249328604102245404235929800458864084518954551745972062570108287204185032269039229976988169294006412650
naive height: 335.8302
Faltings height: 25.9754
discriminant (Δ): -10772711149658527163184661447444210894090439974348883752315017711084626197642728080251675287527330146340366966203606622233476486736465765282500
primes of bad reduction: 2, 3, 5, 7, 13, 17, 19, 37, 41, 383, 34031, 31632505942157258572484507, 5238489305772235654833536943284996847661145129020253404104294215204649761
regulator: 3640236067181175514212463641393.2385576382824244397798531894419360120385381396272592564951257
submitted by: wgxli
submitted at: 2026-08-25 18:56:28 UTC
last updated: 2026-08-25 18:56:28 UTC

Witness: 27 independent points

(-10295743727677338929456267045562550902557501427/4921034630601103214098441, 1085747860368431570600130171537279695026533728900756308681182180222169042/10916530485811499871921431804411690011)
(-41131543512022702658998, -113398403377631746525783050142199379)
(96396503176514251059132, -55918943511130017769000240859653139)
(17367938429890122225477417/121, -51920033881007355353597391044306200474/1331)
(-224015510038493478140388, -126145271298953987954438474913612179)
(9064461178813134226152961577/5041, 853291068640509186377153621656668396422646/357911)
(147107795546870246336089842/961, -1118365722354491234700669573246984540749/29791)
(-6579029050551922674135169562/42849, 1191745809947377820964715080863178986274403/8869743)
(2712259507299167115085381677/11881, -80553986448290381626813747397640173055026/1295029)
(-19605829529691407193434607/64, -35507615696008760736072669113439635173/512)
(-3792459013851332932646054763/11881, 58414369903664520928576814968261560732934/1295029)
(351994858873752277207037, -161126654518492089694087786160037954)
(187771617344395351521262548126388802364/171026420377849, -2498386907728312159512943181701197969767197155474752985097/2236633414960338512243)
(148671115922651702493012194823633585039/470054356863169, 1319627730147913609991027208230730943574087539564062914878/10191124886854512075553)
(12792581706418224288448775247/5041, -1438564502449593303571755935752459030434634/357911)
(1971052813091547821513152380829880247/21512722988761, -5793822259635212964836975450715530729559421015530706934/99779903024734483741)
(1518046420965416119083352588983/1968409, 1764927359630872368775735165897770680950933142/2761677827)
(48668819340504033478567747372019467507608931932081/232913528221050937670664241, 181227852296721739040298919042797510700865516602342003166577950701213564738/3554610924814689389111152013631548997289)
(212328210742363838784246963505116097311/257913514418596, 2939513665167168625270394359409923105458113148815630700071/4142010056719124320856)
(50716268780215703812160325232392753724879382105649/9360026442711885297377344, 360709993953904774466784345798000146721111361409002037619911364526253014549/28636214937136290300191454979642588672)
(2126902876726835594945110588867133008532534128812/2375223206675355762088801, 2969598493819194603324391127869600036397312452342936478964710548771798909/3660636803268913233730462996530108049)
(2162334765921327433443315037538771722515657992980617/17755962481197131475016728241, 107458196869385842015425104988985408089276132643254671207547823934671579906324/2366008649817014057127542073631507380550039)
(26033177248951470678787990682874825659192247/7463298951618056836, 132418354118955140478202832200025902889412917538103573248950004361/20389015557571074490398401416)
(210092168068624445314624474505025159/60396994564, 95998596149235871908462932819350942454572771200993187/14843044590059512)
(3372843001598091323417425421021701213266005253/26725624687177763146801, 191581968225726068339117129894075669269850444663516132105475146283926/4369098117710583350901240782971049)
(15435489366372758103476555382607230844316073732/31193276942774546564449, 1674700165449785876990117227600826615855921424648159212158425191422094/5509237583540261567828235806893457)
(202379963293393376738591263964482077822/1261891557210769, 1664916870359521439581446704833702718880784447114744855973/44826316380544112003897)

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