curve #6441

y² + xy + y = x³ − x² − 19263175019595565662794284246069991501957x + 1028104965204169277247327101875963190791165516806644628049789

a-invariants: [1, -1, 1, -19263175019595565662794284246069991501957, 1028104965204169277247327101875963190791165516806644628049789]
c-invariants: [924632400940587151814125643811359592093921, -888282689936402255537529770216599554660403441123789840470595281]
rank (lower bound): ≥ 25
torsion subgroup: trivial
conductor (N): 1005555187077426390334721557469470704794067246419301318048444714940240322214874780508722230
discriminant (Δ): 847095982182183595826963792625629137608119407173236635981574547476260956068912553280531300443743980653717258536448000000
Faltings height: 21.9282
naive height: 289.8906
primes of bad reduction: 2, 3, 5, 7, 11, 13, 19, 29, 53, 61, 83, 11434389754605246421, 9839168908084260973969394717193082768137066260363766953
regulator: 38696216498905951569377467.25456636440433482660330456980493245717246515331179062470052349
submitted by: apkorte
submitted at: 2026-11-03 09:28:06 UTC
last updated: 2026-11-03 09:28:06 UTC

(73169784752141036347, -101785373186035872502025800924)
(703134763193473759351/9, -63561160237396924007042275456/27)
(52935346761087440167, -395897647574869143597002111944)
(77068643513070811847, 35682595659756651131039212576)
(84422810648753779447, 59605110293266266853553527976)
(322821636799144407247, -5334042344746280038817876415424)
(131262089836771481287, 872462915997706553434758378776)
(179900809106000104367, 1839839164164846462762162917776)
(3670591648303038847, 978492294618235683343457384576)
(68309024856120851047, 176052740800671189883161232376)
(75253186374157639807, 68202821326611247326325688576)
(107099855833189267007, -439883675319394250531959959424)
(-28301260796080069553, -1245234471393704697008419617424)
(66096501526149696847, 208890916115074380720344510576)
(594260561755926711247, -14122367771389804694861087505424)
(74836010206441245097, 75096747559365875575222189076)
(77746670334810305359, -20011876820459343354158005648)
(82188518922383561647, 8526059518172768096722610576)
(76287897151686972997, -50412834996977672611032191674)
(566050957825985120263/9, 6902170792425153470664870237632/27)
(827201819010788519257, -23475882203929957616795766586924)
(118194411841268154637, 634406558955201995651797317086)
(16126391988362155199, -849501790330354339380648598912)
(-124951632203103631681, 1218282187660219021821795428992)
(71816382022260226687, 122853891298390295710078161536)

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