curve #1856

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y² + xy = x³ − 169045115785718437018426173676769180x + 26565003696314398220319291237550041532179599214659856

a-invariants

[1, 0, 0, -169045115785718437018426173676769180, 26565003696314398220319291237550041532179599214659856]

rank (lower bound)

≥ 23

torsion subgroup

trivial

conductor (N)

1013176990175305710079848581901397785469199589474940719468189872476015041794057142

discriminant (Δ)

4301093988771732179028260304215065712888303362456534216451884568248623150125616772208671663849736710520832

Faltings height

19.0964

naive height

254.9600

primes of bad reduction

2, 3, 7, 17, 41, 43, 47, 67, 103, 2237, 7021567391, 157988274616200123163602574743222418210425303275210044069

regulator

41535071571912381579023.0603251863572705190647961401910650339346689260102870795269830

submitted by

Ritik Jain

submitted at

2026-09-25 17:14:20 UTC

later contributions

primes of bad reduction recorded · Daniel Błażewicz · 2026-09-25 17:17:33 UTC

Witness: 23 independent points log in to add more points →

(62114445027933331845368021561695355788096/9595273522436793559369, -15450143868099163732025574564252146607470772844034620906383820/939909499238056211420743982019653)
(198653771032218396568/729, 533671227855111884250532818412/19683)
(512704742495318926072/1849, -2528137327777648548273094654292/79507)
(21192362243419233784/25, -87714713309798786644095272812/125)
(79939367704578115149784/5329, -22593295613800369389870492326861948/389017)
(16973686642147728568, 69909790856139118632282591268)
(1862448236060123896, 2484356342031584284565259748)
(1405778948657255608, -1602200242211776408602441692)
(276742446776707480, 31268953162022229670896676)
(-292370393421611976, -225824796543868113628711260)
(888648958732939166680/361, -26142611105562770187191980512116/6859)
(395255665259388880, -146623964772927504908379356)
(302831918192864756152/1681, -3049805363136513881041625540476/68921)
(1469480397715153392, -1717938382775280316368894996)
(-119207133827136920, 212184856834215076742821876)
(-464180966072774984, -70839645762626720041695452)
(367590698761976020, 118724557981578037769529556)
(134584917027352103992/529, 60687511596774856594932022268/12167)
(213161767618504504, 14720035201804747814587300)
(2278149109616951026/25, 13645803586164055756468892336/125)
(257321193605165104, 10219043471386256738627500)
(3166906980604057645/16, 1876825642107418004648475361/64)
(1331454420470766788819243460671788216/5235046324436014321, 57315378253385726253460936727298785134418805536241988/11977903051180461480164231881)

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