curve #2007

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y² = x³ + x² − 191747767247964355206814272505x − 11254241125408369921622780749124201984607481

a-invariants: [0, 1, 0, -191747767247964355206814272505, -11254241125408369921622780749124201984607481]
rank (lower bound): ≥ 14
torsion subgroup: ℤ/2ℤ
conductor (N): 6116310391204554948397210171493960789901744808779000924864
discriminant (Δ): 396485669632570908790648207546555610319064844722165343841424453935155988422838113658703872
Faltings height: 15.8847
naive height: 213.8915
primes of bad reduction: 2, 3, 7, 23, 43, 61, 79, 103, 157, 167, 179, 191, 199, 227, 229, 257, 271, 307, 487, 619, 1283, 3739
regulator: 20232277810092730176.5767643222396369729123405519131787264753640940
submitted by: Steps Unbounded
submitted at: 2026-09-26 04:59:02 UTC
last updated: 2026-09-26 04:59:02 UTC

Witness: 14 independent points log in to add more points →

(5681425117679611/9, -294860324409185591800696/27)
(-777235595613072763/2116, -301892794339140089868753111/97336)
(1190754047946199243/1849, -914672902438630353884256168/79507)
(-31510222233043025821/101761, -139360087264123766032891749528/32461759)
(131923588055393361947/11881, -1514062907434416382267447136136/1295029)
(10873356306492101085469/1988100, -1130144383311909483102010738238053/2803221000)
(52574608808918357972988281/357512464, -381208125171392047343555580141229590699/6759845669312)
(728013098612600474254755141301/358863087717124, 606095414234838754833650067384187174449398799/6798188215251303010568)
(5657349786355672356256487473069/421839265703076, -13448904465024438152295269952552358624021080013/8664041094316675321176)
(2514732471024638091311283825440981/1737509989831402084, -119950469732311562673821305724995002985981633187631/2290292576285519040267943448)
(50255087718978741884710159882792008109/982640750508331322500, 356249378423921061613618355094098149273332062756894059773/30802939000296575884120770875000)
(3913381358514165433049856736477446753377/5390705811201659491186576, 190690321942503074179363827408614873566459488252509182778439/12516083370950628731103698393503290176)
(17964634375057931750336920719264222028337/1661200699721698956092416, 2405854239736366993173116386857112619938590094562553782068311/2141081298259334546023226223964094464)
(38723735353115083301925462244136876834401/26945593283105675085063744, -7242648811354754855383458166063041839031302887698058508717519/139872270720331081923798772236019926528)

Commentary

2-isogenous partner of curve#35 (David Renshaw).

last edited by Steps Unbounded at 2026-09-26 21:37:52 UTC · history