curve #5953

← home · all curves · JSON ↓

y² + xy + y = x³ − x² − 766429934731552977379645064650427x + 7596848563239270890734215960560899682108411851051

a-invariants

[1, -1, 1, -766429934731552977379645064650427, 7596848563239270890734215960560899682108411851051]

c-invariants

[36788636867114542914222963103220481, -6563677158638729884045496687909174211338333874816129]

rank (lower bound)

≥ 12

torsion subgroup

ℤ/3ℤ

conductor (N)

23854930784364955283661844396465787210564790

discriminant (Δ)

3881957860761395376634126157272771955059123310403123174465850644045024381322345956770304000000000000

Faltings height

17.8535

naive height

238.7715

primes of bad reduction

2, 3, 5, 7, 13, 29, 43, 53, 71, 101, 397, 853, 10597, 50077, 36338257, 104569453

regulator

1006687040041661.7923992456051805707037850221965975289942282228

submitted by

Maksym Voznyy

submitted at

2026-10-26 10:48:52 UTC

later contributions

primes of bad reduction recorded · Daniel Błażewicz · 2026-10-26 10:49:44 UTC

Witness: 12 independent points log in to add more points →

(27661320261852082790851/1142761, -2194611372267905699149149456567454/1221611509)
(33623345946156894287399192299/1700043076449, 927058548985483240874935997504087511047482/2216613065529563793)
(374559068559670777279171/18139081, -58597756947706132285610470230799394/77254345979)
(1799234741094505018147291951/5435523076, 76059468638589390882751978208801424929549/400739374301176)
(2238100739735725829611/93025, -49823182146927615348520345553606/28372625)
(343387284587475406682028691/17273582041, 1057078577365420562605735220468032271986/2270249614066589)
(47339976195043587653930279611/2093898714961, -4093495898174391890960296719008720430057866/3029936351408730791)
(3512351448396158688659/2809, -208109218787867865732241014873902/148877)
(2126318187695233017533669179/44595725329, -83942141366808104646893045472287733747958/9417591487802233)
(258616370954129519740139/5678689, 110888372139986084604050712555869638/13532315887)
(126874277576240900168467736611/6486093461961, 4938490671680167775177598845230806808941634/16518659593146497541)
(125925122188201846653980345895179/1227146929851649, -1365837775408947636168941168588226092805467880038/42987763188236177003393)

Commentary

Voznyy (2026), T = -9985/1638 for the rank-5 fibration of X163 given by y^2 + (9T^2 - 6T + 244)xy + (13T - 90)(22T - 15)(5T + 6)(4T + 15)y = x^3 mentioned in the curve#4645

last edited by Maksym Voznyy at 2026-10-26 10:51:01 UTC · history