curve #3027

y² + xy = x³ − 93016379737949678213737945088754x + 248176820329629460414197205085637112817583889284

a-invariants: [1, 0, 0, -93016379737949678213737945088754, 248176820329629460414197205085637112817583889284]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 5449964496197021254957004621574
discriminant (Δ): 24898423962512792046660013666778186155648619498735623325680799704388820651104353560399195767046144
Faltings height: 17.3957
naive height: 232.4446
primes of bad reduction: 2, 3, 7, 13, 23, 29, 107, 383, 397, 673, 1021, 10069, 132945913
regulator: 175563444.996460777248602114607375887896425325511446068
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:33:55 UTC
last updated: 2026-09-26 20:33:55 UTC

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

(724518345330180, 425634897071619210739518)
(2466343285334784, 183763137126139307726562)
(-243339027083388, -520381520139590912837826)
(-3049210233396, -498458069246280103970346)
(1400661774217218, 347333018067921149283186)
(4923987111172809716/25, 10913426769918985868266471174/125)
(-8315627616507174, -668313957994846830984108)
(189304695352472445/16, 57382453476457944122564163/64)

Commentary

Dujella - Peral (2017). Source: https://dujella.github.io/tors/z2z4old678.html (curve entry 15). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:33:55 UTC · history