curve #4154

y² = x³ − 136644815165959877332x + 625872841693423847583717283744

a-invariants: [0, 0, 0, -136644815165959877332, 625872841693423847583717283744]
c-invariants: [6558951127966074111936, -540754135223118204312331733154816]
rank (lower bound): ≥ 17
torsion subgroup: trivial
conductor (N): 19525073090630769225295212860418607803111169210442560
discriminant (Δ): -5931717204933627690644685666995173050585173206132449728000000
Faltings height: 10.4520
naive height: 150.7410
primes of bad reduction: 2, 5, 7, 31, 223, 499, 2526838861257517569869235285632253094344437
regulator: 5507460687002603.88445189250858409225101767591911419036303850042984023995
submitted by: Andrii Prokhorenkov
submitted at: 2026-10-11 17:18:08 UTC
last updated: 2026-10-11 17:18:08 UTC

(5812034038, 167384352688000)
(5905300638, 157724984078200)
(2009499638, 599499518811200)
(2591678088, 537718550563600)
(22914238038, -3086448389122000)
(10675780898, 619536934893520)
(6075882788, 141189187845500)
(-983355682, 871373859814360)
(-2728317782, -989128147797160)
(7093963638, -116268604799200)
(18685857413, -2144044067508875)
(-11630812222, -801121515184480)
(-6920781962, 1113586807108000)
(6110317688, 138073615661800)
(-2073397212, 948829982474500)
(-12707688362, -556962430334800)
(5434520130, 209229562155328)

Mestre construction: sextuple [-1024, -624, -616, -341, 1240, 1365], T = 368; y^2 = r(x) with p(x-T)p(x+T) = g(x)^2 - r(x).

last edited by Andrii Prokhorenkov at 2026-10-11 17:18:08 UTC · history