curve #1948

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y² + xy = x³ − 431432055927057878448232838906130020x + 110463710536381772191406772584626300067232658913465616

a-invariants

[1, 0, 0, -431432055927057878448232838906130020, 110463710536381772191406772584626300067232658913465616]

rank (lower bound)

≥ 24

torsion subgroup

trivial

conductor (N)

47909354509412505668949498397566458128452979974860964506312503749966917599016167381435480767198

discriminant (Δ)

-131907309486454758953700837219290156622694687361338597681167893142201231432396916366248466127641000812085248

Faltings height

19.3581

naive height

257.7962

primes of bad reduction

2, 3, 11, 13, 31, 3750768886290719, 12158158910567319383, 39498737793812616698480401843431472446539516896161578413

regulator

95745045749307430797114937.627072354038116370195578349788623304594598172154097078367293

submitted by

Ritik Jain

submitted at

2026-09-25 20:01:22 UTC

later contributions

primes of bad reduction recorded · Daniel Błażewicz · 2026-09-25 20:03:18 UTC

Witness: 24 independent points log in to add more points →

(1560971227104659488538917835036378994473004232/2762455174596318318305701969, 31510956059918198719258490312839039221952285247187513803472640883452/145192057426292012585591376486802020788953)
(7703250463416900664/9, 16384190082608218270238886692/27)
(2835347716049102344/9, 2058618817696936523552340916/27)
(-306222228092200382, 462452926381432534635192328)
(-8689065266580650, -337952357296588554271338254)
(731469283215282507886/2209, 6492803521508043514372640587208/103823)
(392810768634132040, -40042133756525503051326116)
(478186211915938198, 116197637748741441077462194)
(36166073535218706091/100, -41669570683380090838890740141/1000)
(17659212577521894856/49, 14502130598414297884482812740/343)
(10858989274378757064/25, 8853779404636938934894686252/125)
(11429315650240837996, 38576968423686765670732908808)
(1172579220340258561689024/1620529, -868221089714424025239071194265345988/2062933417)
(42737406680314726344/25, -261268708403346333098877190932/125)
(3817469596934274153232/18769, -453665522777372780742006424153348/2571353)
(336836071612726102728/529, 3728605941616522643476662402948/12167)
(18267775883946975304/49, -13003972229433228812875671356/343)
(224132089732849810694445797525350521319/13944627696522641937316, 529847310406304622815342676894817812043868475812114100919585/1646684454181315665089582833716136)
(1246276520755096094762777492628021954015477288754552104072/4636374369157327849287593196076497190369, 37240794803419260697396721961511691327986578764657257316707366176491458010153030569692/315695029717192982210010294907148346184830690966571918915153)
(473468078509249418661412246173211404423197497071578254381175539708052870188888/3331413673020431710754134653137455776891383076882063185726809, 1386822608332164369609527324972564405938266039852364589818595513789684085315672559297922070765071947605318708058178468/6080549745197662107760593031114564667482127982397334849606335986947005269652213127989550627)
(6528915534318157532124496859295431724923321596535009927046293789892196041496/17604889709033157261997382035178025555194941634742336010801, 89555160499402421050761799930362127830428337614343651950510740877305670593082641590315276162350762773027649407804/2335876959802436924110220635629433325427190374514025906815433008387685803735319941275049)
(147826935861183358773202930456909770496134452240442681649680084532/358777035404126138275983295535651048046386466889, 11063866290925667447588634128931398114902068957241118399202604025600326635290870853076012968004732/214900267170149227082608860606600972138347364681495048797952860435158213)
(61667435800231972729412828730255486403331673527258953/180788359985233501482621630095431936, 4202403316539193496587438755456756545584083948663431863445119313901647632752253/76869790533936529847671917548035203779614661664034816)
(788609778713705453908541599040263231527320469677164252529426225244853111074006421033957373511229476677663248358193470520968794119872651897231584/2197007267995690898537669137771974934657369801319146257834360719956856361650016624237582792493642835970376985059323205293930625, 140075426762331804680541988903533469943458037560704311212765916084565507974401204303372819837291360995860397988319440885970307124420142277632525879722296770795470574782830560940795363081531254902765397947786689665348/3256471190879661408140876918162745384472685752118805152551019459041698811838464308547849561227158547476439695820325423388058301699144770292957553363106413904255959001113708892201773279890625)

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