curve #1854

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y² = x³ + x² − 9286474923986826171279570792460x + 19356615041645791196531872267946777816479468400

a-invariants

[0, 1, 0, -9286474923986826171279570792460, 19356615041645791196531872267946777816479468400]

rank (lower bound)

≥ 23

torsion subgroup

trivial

conductor (N)

35819382478169004066817345528936202249131130668789846039066817241325534575720

discriminant (Δ)

-110606555832998722030477096825275978976522348905896291580088795583477627581705030471079666400000

Faltings height

16.9306

naive height

226.6819

primes of bad reduction

2, 3, 5, 7, 17, 19, 29, 43, 73, 5581215658969, 259847275952693991576527559572005224841853567845686889

regulator

10239883025727041299873.1379026433922077680198646200983468187820664034092684393908861

submitted by

Ritik Jain

submitted at

2026-09-25 17:14:15 UTC

later contributions

primes of bad reduction recorded · Daniel Błażewicz · 2026-09-25 17:18:09 UTC

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

(206078296304415223973232652829690/156464230318026409, 6003761463219877749208125183438845197368668455590/61890302032592436073761173)
(-579232998242410, -156656658939117767247210)
(-459856324781692, -153394310347263269296236)
(1801975522599470, 92053450230222121680690)
(-575843790419701166/225, 547956727428582820549114298/3375)
(70684926088506314/25, -15663835411966531130545638/125)
(1269694400357024546/289, -1236661395146420206328211210/4913)
(775610299435401002066/97969, 20387621159364191208241319595510/30664297)
(467472418557149866694/7225, 10096417788300798001731699737022/614125)
(-3581102869925986, 81775959257180181505470)
(25782532173634620182/12769, -135646423115876191147166499402/1442897)
(3149755325856850, -146133786030266516355930)
(1041574262328412490/361, 883228224132177805833221610/6859)
(1010103807907435130/841, -2431023280295506624969299450/24389)
(170727147384144275, 70531890836797796926385880)
(1719451352482340, 92046473970609936839460)
(1307255052854990, 97215289710475218784110)
(5378038519486888999/9025, 101570424722138390603254581282/857375)
(-5108613930423414235481134810/3174159134689, 981678637831881810918353612350912398597690/5655135875067212113)
(-2355704046855940700228342151880/1550306599888489, 10565515805969849802377319898723814479015650900/61041668193467173357237)
(-3301251320552626326178877275/2312023645156, 605906275993343001570161022454497084639345/3515510561263633304)
(200771279792409144662174/2082005641, 12908097691206435091080199750831262010/94999835393189)
(506704805807752654390/12321, 11376212640297915984804773980010/1367631)

Commentary

Specialization at T = 32/49 of the rank-17 fibration of X1092 given by: y^2 - (Lx+B)y = x(x+D)(x+E), where B = pq(L+p+q) - pE - qD, L = 337637T^2 - 5806T - 128944, p = 400307T^2 - 728353T - 164164, q = 30116T^2 + 59665T - 51226, D = 20(17239450100T^4 - 50269926206T^3 + 33049656247T^2 - 4679416867T - 19532604), E = 82122368860T^4 + 49706770391T^3 - 201865310888T^2 + 62291384169T + 16126031988.

last edited by wgxli at 2026-09-25 18:30:19 UTC · history