curve #2890

y² + xy = x³ − 13442899747437239752974580x + 18970882127104731286461343053757984400

a-invariants: [1, 0, 0, -13442899747437239752974580, 18970882127104731286461343053757984400]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/6ℤ
conductor (N): 197790703710936583193310
discriminant (Δ): 19834808732792188728990275118497597034101452366670295672224364343296000
Faltings height: 12.9391
naive height: 185.1951
primes of bad reduction: 2, 3, 5, 7, 13, 17, 23, 79, 197, 283, 347, 3203, 37853
regulator: 1101464.461219221194436651404736734268545006488582142
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:27:03 UTC
last updated: 2026-09-26 20:27:03 UTC

Witness: 7 independent points log in to add more points →

(2473914318080, 924811798245255500)
(2139183350950, -56421828041053070)
(2261028565640, -367486467194481460)
(3914994703590638/1849, -59783678444937779656/79507)
(2135862463622696/961, -8001969812854331580748/29791)
(177220049410771610/85849, 3314351283378990682621990/25153757)
(1371555317480, 1764460129371065420)

Commentary

2-isogenous image of D-z6old678-124, rational kernel x=-1058632940440. Source: https://dujella.github.io/tors/z6old678.html. Independent witness points transported by the degree-2 isogeny. Witnesses saturated by exact rational halves of published and transported relations; quadratic-character independence is certified.

last edited by Natanael Wildner Fraga at 2026-09-26 20:27:03 UTC · history