curve #3197

y² + xy = x³ − 7372911492530406268416156245x + 243594391906613268628507257344604677608161

a-invariants: [1, 0, 0, -7372911492530406268416156245, 243594391906613268628507257344604677608161]
rank (lower bound): ≥ 14
torsion subgroup: ℤ/2ℤ
conductor (N): 300953424448851386334317567807295829194402996102
discriminant (Δ): 16456496382158491567571999599780229982446629358546306631487625189864201625638141952
Faltings height: 14.7432
naive height: 204.1164
primes of bad reduction: 2, 3, 23, 29, 71, 73, 101, 257, 307, 353, 449, 1181, 3511, 4217, 16561, 204751
regulator: 1433640315429031.36780115455167272376676320979852644640705991918673
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:42:12 UTC
last updated: 2026-09-26 20:42:12 UTC

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

(-72376481830226, -630940588803637101569)
(56312693537242, 83547350623177255879)
(50545746944914, 7938107321308587511)
(-24664074799982, -640653456150957147401)
(48768170604178, 4243475038421673079)
(44275623883186, 62841111181852200343)
(44033644751050, 65709829875594008719)
(48781448921950, 3856666655607214531)
(48831932859328, 1852759677330985393)
(226433646572535934/361, 106787838011896189595371765/6859)
(153942078863442, 1660342552186148579319)
(2829817753498450/9, 145424908163363854584413/27)
(6692769349018554/289, 1434645063716592596334423/4913)
(270782451612808972/1849, 120702043132790721191878453/79507)

Commentary

Dujella (2001). Source: https://dujella.github.io/tors/z2old141516171819.html (curve entry 54). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:42:12 UTC · history