curve #3090

y² + xy + y = x³ − x² − 28562016892450236469278130528841147x + 1855604032124054096684337837801147788788173909411371

a-invariants: [1, -1, 1, -28562016892450236469278130528841147, 1855604032124054096684337837801147788788173909411371]
rank (lower bound): ≥ 10
torsion subgroup: ℤ/4ℤ
conductor (N): 739676219036898857957413188000804190859490
discriminant (Δ): 3745667525283503499761187017373613355048815419084552325267964531485308997497851238001327504641600000000
Faltings height: 18.5840
naive height: 249.6258
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 47, 101, 271, 2153, 14009, 26833, 778360019
regulator: 347978520.9821089362661229244539122160141524532668602233083
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:36:48 UTC
last updated: 2026-09-26 20:36:48 UTC

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

(-35654245600770339, -53184928493164853355793706)
(102663271430755911, 2319240609938111081641294)
(52673995966314411, 22299665827759615565408794)
(91736654652562531, 2727711406692375247325914)
(100595198949492411, 603919072698101752016794)
(-65816389876514589, -58739676675009736575030206)
(104943321056725411, 3736640023782459047249794)
(85100033778102759, 6424267594322106960581806)
(109620193709308971, 6472309265284227861714874)
(131809366710013161, 19516154123990917016704294)

Commentary

Eroshkin (2010). Source: https://dujella.github.io/tors/z4old9101112.html (curve entry 32). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:36:48 UTC · history