curve #2949

y² + xy = x³ − 2458494060302392145867072081685252395150x + 64836302371010468053563961422511164548489508727209655522500

a-invariants: [1, 0, 0, -2458494060302392145867072081685252395150, 64836302371010468053563961422511164548489508727209655522500]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/6ℤ
conductor (N): 5360073200986915269158012602792104734070
discriminant (Δ): -865003104665697317366768650959123545956852676938822778320321891616784106042102267405522106528362109727799507249539000000
Faltings height: 21.7180
naive height: 284.3616
primes of bad reduction: 2, 3, 5, 7, 11, 23, 29, 47, 61, 97, 101, 109, 151, 727, 1063, 2707, 3571, 7681, 131143
regulator: 2578359876.10585668404104538730823983323782097398111220
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:29:43 UTC
last updated: 2026-09-26 20:29:43 UTC

Witness: 8 independent points log in to add more points →

(43155499697406724159576/625, 7399831333312344070346106716218726/15625)
(-22883762348251578050, -330321713827001137778136788900)
(-548648125152481694, -257264426955158632651117708328)
(154591304487277414540709200/1079521, -1825692024376487379987807495255690705950/1121622319)
(-1080163835584214166092666/54289, 4115903623771839840402016120509527894/12649337)
(-159705102986780530265696570/2699449, -251261318335932108099008095921699664500/4435194707)
(-21988967777062815197600/961, 9840517216384251577948579839279250/29791)
(425159882099985247297390/326041, -46218267119142302327661259147365437390/186169411)

Commentary

2-isogenous image of D-z6old678-039, rational kernel x=29778866334177098428. 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 20:29:43 UTC · history