curve #4591

y² + xy + y = x³ − 1078873095503935828532905773x + 13624668746810382060185388457278998611256

a-invariants: [1, 0, 1, -1078873095503935828532905773, 13624668746810382060185388457278998611256]
c-invariants: [51785908584188919769579477081, -11771713797244247778863051910468709169341021]
rank (lower bound): ≥ 10
torsion subgroup: ℤ/3ℤ
conductor (N): 937937625235846068118709835889853830
discriminant (Δ): 176611793261384048424478841035871534552430271729164647141571086687390792843750000
Faltings height: 14.3061
naive height: 198.3507
primes of bad reduction: 2, 5, 7, 13, 47, 53, 89, 101, 211, 1123, 575212549, 337720088071
regulator: 572211760511.3225781387875034401757552594997490893585806657
submitted by: Maksym Voznyy
submitted at: 2026-10-18 15:15:26 UTC
last updated: 2026-10-18 15:15:26 UTC

Witness: 10 independent points log in to add more points →

(26869333462010895, -4404382382025142110090698)
(6259891776802361116655/320159449, -12710369079935690909400123790486/5728613020957)
(968520045912364535/49729, -2820765602047827469410566/11089567)
(2240534311702865440455/42601729, -88959632144623270316890718153734/278061485183)
(208823623451263561193998535/905909914849, 2988556762527764531821484993266181859814/862238715583874257)
(13175510710844483/529, 571203537444268065306398/12167)
(2411662280405145093670/119661721, -10737391548718414117823123864762/1308979566019)
(1641775500168070/81, 6686377160946661907983/729)
(47767897702797745/576, 9721158139606698903939973/13824)
(331246613860492749343030/16946051329, -4713028938094815164835985272584409/2205986123855233)

Commentary

t = 17/228 for y^2 + (7t^2+309) x y - 91 (t^2-1)(t^2-25)(t^2-121) y = x^3 from https://github.com/Layr-Labs/elliptic-rank-challenge-public/blob/main/submission/board/3-r12-z3k3.ec

last edited by Maksym Voznyy at 2026-10-18 15:15:26 UTC · history