curve #3056

y² + xy + y = x³ − 19268651287520295734172617502244x + 32555553942033212710586516699879290958187545426

a-invariants: [1, 0, 1, -19268651287520295734172617502244, 32555553942033212710586516699879290958187545426]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/6ℤ
conductor (N): 1537557927687420856077617546790
discriminant (Δ): 1027587137130271525920944449534041253598570604442581009178061565013457188476786339600
Faltings height: 16.2906
naive height: 227.7217
primes of bad reduction: 2, 3, 5, 7, 11, 13, 19, 29, 41, 43, 59, 61, 73, 83, 107, 127, 977, 182057
regulator: 6973135.36811254893874616314914227735354294620759989747
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:35:13 UTC
last updated: 2026-09-26 20:35:13 UTC

Witness: 8 independent points log in to add more points →

(2140883341156045, 33408148409468593971467)
(2533820973458533, 45331337312131766243)
(2540709721186549, 555563200532839538387)
(2534229790601908, 9684394686284923493)
(2534377191793933, 3158038739286397223)
(2533846600502521, 43096907321293963667)
(-506801237403755, -205403893647732916078153)
(4318476084514441, 172860121954632936055307)

Commentary

Dujella - Peral - Tadic (2019). Source: https://dujella.github.io/tors/z6old678.html (curve entry 25). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:35:14 UTC · history