curve #340

y² + xy = x³ − x² − 4478863882000398277272391296x + 114808464561400729459593498162805258984396

a-invariants: [1, -1, 0, -4478863882000398277272391296, 114808464561400729459593498162805258984396]
rank (lower bound): ≥ 20
torsion subgroup: trivial
conductor (N): 41455086380717191185808070125299852614948356707622719536837037239971384494
naive height: 202.6211
Faltings height: 14.7200
discriminant (Δ): 56023261274818083684317895593068832776592402076388197065657911137049675053251242884
primes of bad reduction: 2, 3, 7, 11, 67, 907, 492189681146015024152899098930855972467406576319834595366987250491
regulator: 107950823401904672275211.002789114996797764365608600685292758274805529213099082
submitted by: 7fff-zip
submitted at: 2026-08-24 19:19:00 UTC
last updated: 2026-08-27 02:22:31 UTC

Witness: 20 independent points

(3959568700584289293/117649, -1888919593160911716243688163/40353607)
(5983705942679832815/229441, 13788091865318344243182730294/109902239)
(2881285059776627, 154619119609581457020302)
(22604263646403854/625, 178019179057919383520258/15625)
(2501120224508696966/13225, 3735278267807866710637937216/1520875)
(493011317715364/9, 4966708714634479141658/27)
(2535873207907338494/12769, 3833338061428204981266167200/1442897)
(2621178175745556434/124609, -7606344775984294549796004152/43986977)
(-1775646997704119939/90000, 11937974612173216911789469159/27000000)
(47472459163994606/961, -3537936341989803306725536/29791)
(1567034501871269/49, -22441168132146613189600/343)
(55057542053675, -187379238442397134714)
(3723652938785579822/63001, -3760784743567895785576713248/15813251)
(36382667185742, 3889906867339569056)
(7009771369859069/1369, -15364593903761431271204353/50653)
(30648985263139943/289, 4482910575592089590018818/4913)
(42964988388252, 41074040348284017802)
(-1171933235298, 346490670641813751746)
(241380362084270276/6889, 17081211134823369727885090/571787)
(39884876978403068/529, -5518539512833845202863266/12167)

Commentary

New in this search: Mestre quartic family with roots [0,113,550,753,868,1058], T=1889/7. 19 independent rational points certified exactly by Cremona-Brumer quadratic characters; quartic point box [10000000,10000].

last edited by 7fff-zip at 2026-08-24 19:19:00 UTC · history