curve #309

y² + xy + y = x³ − 139247897426027149067804108174260263825601x − 12171148262466750740691943470052015013728330466029726884498652

a-invariants

[1, 0, 1, -139247897426027149067804108174260263825601, -12171148262466750740691943470052015013728330466029726884498652]

c-invariants

[6683899076449303155254597192364492663628825, 10515872098771272639947813309510267017128395626861137289211391875]

rank (lower bound)

≥ 17

torsion subgroup

ℤ/2ℤ

conductor (N)

14736232836353426730586889330999407111621750064300242106070930802493850

discriminant (Δ)

108805746048883061193612306928010127310531083533286108872721769647652556904158900879842993759008627125609908132164015812250000

Faltings height

22.6927

naive height

295.8248

primes of bad reduction

2, 3, 5, 7, 17, 23, 37, 41, 67, 79, 97, 101, 103, 151, 229, 389, 857, 977, 983, 1499, 1531, 11719, 12907, 49639, 938573, 4153367

regulator

3763594023177061562764041.52676164241850735091184955799828624531403044313

submitted by

7fff-zip

submitted at

2026-08-24 00:23:34 UTC

later contributions

rank ≥ 15 → ≥ 17 · David Renshaw · 2026-09-02 19:09:02 UTC

Witness: 17 independent points log in to add more points →

(417476533381735876627, 1567389922384548369235256786486)
(8574627594145380504727, 793244472541824353863163965729886)
(13580713215478598882323, 1582044898758012321734234287864694)
(-579086355887642860478262683390121361828937/2815956789300903787009, 416473599189635033074574707180567003457802413016640488890067842/149430407039227622708317738166527)
(-15112469804421821324395989268429784945813/55596090396779830921, 980541397336396757305438486275377930000916962149362289379294/414539938457617967843292450469)
(-2588879946641569821627283496103873302/14921992321538449, 4741164728733509144077154430765557711370163714588754998/1822805029686868411433543)
(-227694818089805014684197197478071474/2131917763563025, 119859648377655947015677344508528337950472316063188189/98436388662077666602375)
(-213293129493828877917353/961, 83208523138046682258484816354057826/29791)
(-6831837002591247631847/64, 622205546465850731255887962212257/512)
(35729115842572740083857/64, 4694856465890330255585827438133083/512)
(45217890518455797390553/64, 7967061107616441418701898358185207/512)
(56977374367393099737748/121, 6873807448664480639001543470845729/1331)
(346002499441700055197692/121, 201731669795856202671162628019538241/1331)
(4010446973304367153050763/169, 8030364686397976757935409794061557742/2197)
(1033945296878027100215607905914/745017025, 1010141377501971603702052459523516833382862422/20335239697375)
(56720485590760159681632717757483/112709932729, 254401205881160311515987354598056602578324088362/37839316745578067)
(2044324683292361954819418867346209463/360429351690529, 2916542549443548774784151644107787151634919359199440958/6842742951969604182833)

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