curve #4627

y² = x³ − 73383668296922087936770972212342095007x + 315959424020043283262823199702825508252377711450513072130

a-invariants: [0, 0, 0, -73383668296922087936770972212342095007, 315959424020043283262823199702825508252377711450513072130]
c-invariants: [3522416078252260220965006666192420560336, -272988942353317396739079244543241239130054342693243294320320]
rank (lower bound): ≥ 17
torsion subgroup: ℤ/2ℤ
conductor (N): 98117440630487479334471813728300734607596692047552312523454585839592
discriminant (Δ): -17835002582085889924364627186041943755473998566441992219680676665879667061341925431982970675076235518317607712558848
Faltings height: 20.8231
naive height: 273.7136
primes of bad reduction: 2, 3, 7, 11, 19, 59, 79, 89, 109, 127, 331, 503, 877, 883, 2207, 4651, 4831, 5641, 8761, 60373, 110051, 161059, 6072527
regulator: 52358272771235627846.3765762729653116709298607604409448374880084972427413
submitted by: Andrii Prokhorenkov
submitted at: 2026-10-19 03:31:22 UTC
last updated: 2026-10-19 03:31:22 UTC

(-9676025225793647947, 10958982458918741732934951194)
(-9427002956908254713, 13037827895557153622409046032)
(-9215124540669684731, 14479790269648307439074613066)
(-6690025634053701683, 22527234521648352105607241118)
(-5533557110521812731, 23507301368687938708132303434)
(-203312762424384223, 18189855859402564346835143318)
(7688967279628234759, 14362737206525192623768627536)
(8200620912844775623, 16299111606048756863824957056)
(9335867444812888369, 21084560437612855911553191366)
(12764347888100361943, 38196096533837092987602121656)
(36235519050369309907, 212684192928033428638529938368)
(6566233515368022932329/2304, 1260790689785905805672334769680331/110592)
(71698208767978325708761/15625, 17009506655818338842994942963354366/1953125)
(174969117606347591246233/1369, 73029342403829776468471407000859554/50653)
(705446934179068756603597/53361, 501668702539272749645812064647821662/12326391)
(804360978793349297143761073/8826841, 22716450532857031400788829306465471250534/26224544611)
(1384326916224470350885898281/61418569, 48403128250807829545064139781328856744018/481337325253)

X660, T=-1545/118

last edited by Andrii Prokhorenkov at 2026-10-19 03:31:22 UTC · history