curve #3100

y² = x³ + x² − 50491061391988204405194159029361x + 135663699587915859546796760459040265253947368735

a-invariants: [0, 1, 0, -50491061391988204405194159029361, 135663699587915859546796760459040265253947368735]
rank (lower bound): ≥ 10
torsion subgroup: ℤ/4ℤ
conductor (N): 734580525126326665789875840301734560160
discriminant (Δ): 287227788416171964052592741197803220249640544884577783048023107766357252867321277264824644300800
Faltings height: 17.1079
naive height: 230.6117
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 163, 199, 229, 313, 1531, 18541, 53173
regulator: 194976137.5156453956588906749476380118405280882247160821410
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:37:17 UTC
last updated: 2026-09-26 20:37:17 UTC

Witness: 10 independent points log in to add more points →

(594879530959527, 325327708047053156882580)
(2884705001402037, 118393501187363110445880)
(-1520096210813991, 457058525564559582882036)
(2775663697578585, 130007938722486060873780)
(-1133633732800665, 437544521662602852957420)
(4540694038684071, 4338712096157000607084)
(-2587491423319143, 498984311740534566303060)
(16514120392102887, 1950773163564108331686420)
(3618616115188602, 18424847821955205003945)
(1321489924618677, 266923276622854745030280)

Commentary

Eroshkin (2010). Source: https://dujella.github.io/tors/z4old9101112.html (curve entry 31). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:37:17 UTC · history