curve #1846

y² + xy = x³ − 65256837777298833093656552012343913x + 6401977826288532075622059937777863791754900228899417

a-invariants: [1, 0, 0, -65256837777298833093656552012343913, 6401977826288532075622059937777863791754900228899417]
rank (lower bound): ≥ 21
torsion subgroup: trivial
conductor (N): 2510926671941104410738622226641345793578528665792687578402154433100167950
discriminant (Δ): 79512862356775502662530873270874137905968691905044031046676098955814701727631171907078306153414574080000
Faltings height: 18.8124
naive height: 252.1045
primes of bad reduction: 2, 3, 5, 7, 13, 17, 29, 41, 47, 53, 61, 71, 487, 881, 1451, 12703, 2432597, 43849025326375441049247113091207426373
regulator: 45258913682489850170.768060383434676208468378761785925859740092268759139906659231
submitted by: Ritik Jain
submitted at: 2026-09-25 17:09:37 UTC
last updated: 2026-09-25 17:09:37 UTC

(133837532185872018364257199531414925087738/186345321748683735141529, 46211583505302547337739967229137981614864273080275541300950057/80441051924489722580692294422342083)
(1860248236578651247/4, -2214691096380873784393447159/8)
(16267666037104153402/9, -64990037788030810442953095055/27)
(293707930899601706, 112125154858217386736381939)
(164591006735811322, -10958668259946435015866621)
(-507439686949551965062/2209, 9996519972657763092436974912877/103823)
(-209859980532517558, -104183917841674853336272861)
(80891973004196243/4, -570785273773625387038318373/8)
(-3251466761494652686/25, -14080804440566914345508512697/125)
(-271606264923582598, -63951228485234395605103741)
(654285917214637924826/4225, 872830894474752281950641455779/274625)
(84089527627596011642, 771100291977914516203407746819)
(395900648683822910294522/1620529, 146461659671448829664753211903436859/2062933417)
(109375116080120982386/25, -1141965165065860083960874506881/125)
(2894049609779102357594/18769, 6215766276990131112068498122315/2571353)
(90451015695370000448/529, -189637673651577811131011045507/12167)
(7672752553297496702/49, 1646284061484610290753518285/343)
(-59395219266654598, 100341357560338483741982339)
(1230852645810785098/9, 160423674409814001598232273/27)
(-61403995443033320374/961, 3025034716482902524407061678589/29791)
(-17987008997743965106520273722198/70171230587929, 46608174646101561154417330349410432316774849545/587812259012189521283)

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