curve #2184

y² + xy = x³ − 9978082456644606532120457534482336270x + 12118558737989607267350601135758073759160572299571620612

a-invariants: [1, 0, 0, -9978082456644606532120457534482336270, 12118558737989607267350601135758073759160572299571620612]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/2ℤ × ℤ/8ℤ
conductor (N): 254711946927568865593530
discriminant (Δ): 136815558058183714799292060601468673257315273517022332204047654092804848840545882480083862841450718731886240000
Faltings height: 20.0423
naive height: 267.1940
primes of bad reduction: 2, 3, 5, 7, 17, 19, 47, 73, 313, 5503, 14593, 43543
regulator: 403565.96025226647030402892142366643030117602
submitted by: Tom Fisher
submitted at: 2026-09-26 17:25:32 UTC
last updated: 2026-09-26 17:25:32 UTC

(64935066190938207177379921809620324336417876/38334673696173434639203369, 65856901684133496078852002264730967351861454596251807552291945974/237349136666849357523634570372143855403)
(12778692524551274601846592078841174742602753512/1745809761812003076444759729, 1327613229257136573838681932815478197257627319929587909972495605591642/72944974419623675473252095060997029084567)
(359051941184400968436675916287612822567566985575036/33554076578440432506346355899225, 6535484414783710408702686612744978642320928319784476158335695253889445283914/194364943774259187095447069125475692174244412125)

Found by Fisher (2009)

last edited by Tom Fisher at 2026-09-26 17:25:32 UTC · history