curve #1968

y² + xy + y = x³ + x² − 589025559248347644593036545910x + 229982091065291757573366600952007264582275187

a-invariants: [1, 1, 1, -589025559248347644593036545910, 229982091065291757573366600952007264582275187]
rank (lower bound): ≥ 20
torsion subgroup: trivial
conductor (N): 23340722393802212613784118025982959116445074784037922061026509016310
discriminant (Δ): -9770004713492275669484845522077345306135327194507236449048414985209753546048952134144000000
Faltings height: 16.1668
naive height: 217.8163
primes of bad reduction: 2, 3, 5, 7, 11, 29, 43, 83, 107, 463, 1970575136608747254846001985401770110765803206644097961
regulator: 3794835604485135148.04588426036346748902544241682549682751425695588596180017857
submitted by: Ritik Jain
submitted at: 2026-09-25 20:07:09 UTC
last updated: 2026-09-25 20:07:09 UTC

(8499547917931896613/144, -24777487602783269458665997847/1728)
(-716345797739983, 16862215409730062388991)
(276095287774721, 9402194777047514653199)
(768925212129187461497/52441, -21293462979796426729724308629901/12008989)
(2460247370433553/9, -255278942412285544320643/27)
(3494723396906177, 202120946508489639854351)
(3489495293902507023/1369, 6263228062150719768415765873/50653)
(5351102538660800517, 12378411187712894281165410991)
(1798869830666224521, 2412679130400153145810987759)
(9952927335816047787/10201, 24900162538820184673454971751/1030301)
(41230901985100159537/12321, -258525390874256320534669141999/1367631)
(579840056908642153/9, -441501000650797853828923243/27)
(95169058717610923473/97969, -734970364066501392363346315673/30664297)
(142963197595786369/289, -37946548528642468256814113/4913)
(3031919934546307177/5041, 3456825213770704051302481681/357911)
(155366174045306678857/68121, 1843463784868234400747128391171/17779581)
(6934290548780053/9, -412608323291151372249643/27)
(1274147418751827086317727466102028947/2991379792077663357361, 1228361581441280472935167550830857054130966263029168209/163609053898029285487190476837609)
(39032571535997694282250003568601100749907657/32522553448881496366461751296, 207511193667066476696671500431965587365042511922649552317180037221/5865120701807912408653896918169859247046656)
(6544845994906532016109448575/14915638753929, 431104779210802917554953720528809394111199/57605345371857850533)

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