curve #2741

y² + xy = x³ − 16400025787674584384351661191487963752312085x − 25561782006523039516185003319420734002994403197442467557859875775

a-invariants: [1, 0, 0, -16400025787674584384351661191487963752312085, -25561782006523039516185003319420734002994403197442467557859875775]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/10ℤ
conductor (N): 145604394817456968019313610
discriminant (Δ): 30917567091387480737857713044595196987127245843339613487891696172504140466966573303001185096871124019617496612966918945312500000
Faltings height: 23.5214
naive height: 310.1312
primes of bad reduction: 2, 3, 5, 7, 11, 17, 19, 29, 47, 67, 103, 281, 1601, 4639, 9941
regulator: 6893292.193206142453126276958466258423278432124
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:20:13 UTC
last updated: 2026-09-26 20:20:13 UTC

Witness: 4 independent points log in to add more points →

(560800305298961112242967263264308598619934470/110938726655373994125841, 5317508408962916894864354493967670638396096962480036599091378444885/36950878248768628381659856146805639)
(-2107528900578169337142897396849771314520/896894692288929049, -560701051282223037158350977777240128119395740283828101445/849399851804179037419963907)
(-2887559979329970478190882138132026080/1227597605593921, -648763997038520150451322090131852499051109117680065/43011446563381107935969)
(-479729120746750991858205231239493993505893410881009573680/205412986298907122030093349843878041, 108188300450679158661255825766767169249658535695661808322078887591016956908951528765/93098320130106531230382738329689024717127165572457411)

Commentary

2-isogenous image of D-z10-017, rational kernel x=1176102565155133244818. Source: https://dujella.github.io/tors/z10.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 20:20:14 UTC · history