curve #3190

y² + xy = x³ − 47847763372758290648644402243255x + 127351524490807893375157005788342713513098443177

a-invariants: [1, 0, 0, -47847763372758290648644402243255, 127351524490807893375157005788342713513098443177]
rank (lower bound): ≥ 14
torsion subgroup: ℤ/2ℤ
conductor (N): 159345113070803533282965684718748208769606387290
discriminant (Δ): 4403290465984192988125239632232010181390860565264707581305438684884716208687883259000000000000
Faltings height: 16.9370
naive height: 230.4503
primes of bad reduction: 2, 3, 5, 7, 23, 61, 73, 79, 101, 149, 263, 421, 547, 701, 757, 2719, 3863, 406591
regulator: 1265431023732111.96634211619194670978702297613916568632800003153549
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:41:53 UTC
last updated: 2026-09-26 20:41:53 UTC

Witness: 14 independent points log in to add more points →

(2402192630678294, 162092266368711928387253)
(-3391843101653806, -500621445843756363450847)
(3898541733166694, 8216220130453507683653)
(32377754126076766/9, 1138429748985801612624391/27)
(390366006792027974/121, 107844827632800665778236143/1331)
(-163904684517556, -367681375287588486702097)
(4075783435005734, 6431233972466766702293)
(4280103056359694, 31089897478920261972653)
(16470707761625651/4, 96727117093963215845599/8)
(9925993664878474364/1681, 15518946541291953916348858663/68921)
(19820967570789886694/5041, 828900104352225901270695523/357911)
(3933675401213972, 1693998224614066185845)
(4431526619262194, 48384960945654700025153)
(487580757398702435654/841, 10765620460399382973566818211017/24389)

Commentary

Dujella (2009). Source: https://dujella.github.io/tors/z2old141516171819.html (curve entry 71). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:41:53 UTC · history