curve #6154

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y² + xy = x³ − 185883539974518800709005066562964625x + 30915007146636844887369162642051089599270566414515625

a-invariants: [1, 0, 0, -185883539974518800709005066562964625, 30915007146636844887369162642051089599270566414515625]
c-invariants: [8922409918776902434032243195022302001, -26710566174694233996070571400897495064818134174674953001]
rank (lower bound): ≥ 22
torsion subgroup: trivial
conductor (N): 163315887498011033904052380947944439698574540101013825804628623437509570
discriminant (Δ): -1820981632136752132260128249971009286646995170115002794391058708341031063543092050991050399294504960000000
Faltings height: 19.0739
naive height: 255.2493
primes of bad reduction: 2, 3, 5, 7, 19, 23, 41, 79, 83, 89, 127, 547, 1277, 37049, 22630295334151631667073569676775657465610251801
regulator: 82335485314170100104.87175327483144965010823324137892402654614681026343528196499272
submitted by: Ritik Jain
submitted at: 2026-10-29 13:48:38 UTC
last updated: 2026-10-29 13:48:38 UTC

Witness: 22 independent points log in to add more points →

(-311134690654546394300/841, -5401398402376005150040124173675/24389)
(82554914576572388650, -750081558176714511163974971525)
(67266912204275431449978463599226563192593340250/215630180798784289967583663289, -5739726435802671884864083153705107753044559426651262594441326326585375/100130024068657879215722024815596818919630163)
(14038320323126056000/49, -11761030593552999191986455125/343)
(7882493113636025884/25, -7553102259037280903139130033/125)
(11606855373786063490/49, -4535536377605960645498089355/343)
(3401153376316434080650/2809, -187191657322012886276558748618625/148877)
(-470499239711497250, -119242918504110010951204625)
(263981088093698652250/361, -3668159800459952212535203220375/6859)
(-461171560995458150, 136226307476907355844975275)
(85985655986969290, -124769494763727445063409765)
(6952186364746784266/25, -3373521836948853202285430401/125)
(-8052843154503605150/1681, 12291413284745593529121756102875/68921)
(5891937780403998724450/22801, 40197689223996096342532150638925/3442951)
(-5978506705898222870/49, -78049204515544299982067161235/343)
(1366888645397969770, -1526665176640419196462955045)
(1265913045344425124750702074/8012935225, 53153779789989391573130204973458764661377/717277896665875)
(251356952464481430730, -3985067801739849290601791292005)
(910529359495937201530, -27475201250441012791238794740725)
(83299150752800788666/361, 120552595634892467744684391433/6859)
(172736046029003464000, -2270246997255394616739305178125)
(440225083789450673530/1849, -988560917418510871451482857215/79507)

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