curve #2888

y² + xy = x³ − 2446710621837950490885310x + 3241325835579095396775139751584108100

a-invariants: [1, 0, 0, -2446710621837950490885310, 3241325835579095396775139751584108100]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/6ℤ
conductor (N): 1181838693760983713230230
discriminant (Δ): -3601269305564080125392954307880944095127910098257218454783357376000000000000
Faltings height: 13.1866
naive height: 181.6612
primes of bad reduction: 2, 3, 5, 7, 13, 31, 41, 47, 61, 71, 157, 1039, 10257671
regulator: 354542.8912654179008853453424240555888648594512467304
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:26:59 UTC
last updated: 2026-09-26 20:26:59 UTC

Witness: 7 independent points log in to add more points →

(2057938690220, 2630920009494099890)
(1128694977782639680/1026169, 1425620760799407400291095830/1039509197)
(-1825530227680, 1274434081288494290)
(44591928273970, -297594569683082696360)
(-185989622606020/121, -2443562290197981770570/1331)
(2082444617720, -2678968185132140110)
(-6340420838098691581256740/3854817830161, -12700223906241336521440652080058993950/7568429828385372409)

Commentary

2-isogenous image of D-z6old678-127, rational kernel x=16111853758239/4. Source: https://dujella.github.io/tors/z6old678.html. Independent witness points transported by the degree-2 isogeny. Witnesses saturated by exact rational halves of published and transported relations; quadratic-character independence is certified.

last edited by Natanael Wildner Fraga at 2026-09-26 20:26:59 UTC · history