curve #3104

y² + xy = x³ − 38690898580374797692832240x + 71645473412331804273266091664555065600

a-invariants: [1, 0, 0, -38690898580374797692832240, 71645473412331804273266091664555065600]
rank (lower bound): ≥ 10
torsion subgroup: ℤ/3ℤ
conductor (N): 2595803905868706552568205926928490
discriminant (Δ): 1489374127538416768478441778520288296944405332560416155670850260619264000000000
Faltings height: 13.7120
naive height: 188.3665
primes of bad reduction: 2, 3, 5, 13, 19, 29, 37, 61, 67, 571, 139898547573624998209
regulator: 85830640.77008136881940944096515022856634153033585944253840
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:37:28 UTC
last updated: 2026-09-26 20:37:28 UTC

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

(2020834202080, 1307747476141906960)
(-1413936357920, -11114187406056493040)
(2042874944830, 1063208190423500710)
(34040558580, 8386206101214516960)
(-774541703840, -10057262105626179440)
(-204110181920, -8918193455655853040)
(4977572386272, 1544079016781181456)
(1754121626080, 3028903739399506960)
(4911027872730, 280209611489120460)
(2054214947920, 913467905280053920)

Commentary

Eroshkin - Siddiq - Voznyy (2023). Source: https://dujella.github.io/tors/z3old891011121314.html (curve entry 47). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:37:29 UTC · history