curve #2036

y² + xy + y = x³ − 6444802130025859084423x + 199125288161224641980320054413006

a-invariants: [1, 0, 1, -6444802130025859084423, 199125288161224641980320054413006]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/6ℤ
conductor (N): 140409740846986028110 ☆ record for ℤ/6ℤ torsion, rank ≥ 7
discriminant (Δ): 2846201347341256110799562151707518112115773873184878377929687500
Faltings height: 11.2121
naive height: 162.2663
primes of bad reduction: 2, 5, 7, 11, 17, 19, 23, 179, 271, 2677, 189019
regulator: 77983935.05766977332141749639190586215246586067599173
submitted by: Steps Unbounded
submitted at: 2026-09-26 05:05:11 UTC
last updated: 2026-09-26 05:05:11 UTC

(-666949466870/9, 443459856219083104/27)
(268376450055/4, -66332379824463459/8)
(2681674165406005897830/56971483969, -3221919029258854654568706799269/13598352594108703)
(8761139845468778557566/40865026801, -769273834975766409367026672484796/8260906032848951)
(10221168754234351366129/7619194944, -1031549231533496091053242649835467/665064288271872)
(11097528735884779020/17901361, 36673405763902430166247103682/75740658391)
(500910411474842139765467756213745/91284711471956463616, -11209699233982180944308176536635976237608485176553/872161819690922651894852878336)

2-isogenous partner of curve#1262 (hdeping).

last edited by Steps Unbounded at 2026-09-26 21:48:55 UTC · history