curve #1804

y² = x³ + x² − 74530617488056778952761233x + 245185753017741419396996325830805323663

a-invariants: [0, 1, 0, -74530617488056778952761233, 245185753017741419396996325830805323663]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 2844169076472523644089985600
discriminant (Δ): 526097771148505346288857643147894229392933850856736037828276515922852096000000
Faltings height: 13.7262
naive height: 190.3334
primes of bad reduction: 2, 3, 5, 7, 19, 23, 29, 43, 53, 59, 67, 79, 167, 181, 251, 1237
regulator: 985047.2271552602686278666491316484650900871117919551
submitted by: hdeping
submitted at: 2026-09-25 15:05:29 UTC
last updated: 2026-09-25 15:05:29 UTC

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

(-2917266958717, 20923293632348746800)
(22726622167733, 101437873912668087900)
(3204220228483, 6266662372787115600)
(8818701660773/4, 76560444874866865689/8)
(-7516642360597, 19511948002341765600)
(13189002527954, 39451558144614437619)
(-9559476965653, 9169517776895092512)

Commentary

Rank-7 specialization (w2,w3)=(-76/3,26) of the Dujella-Peral family of curves with torsion Z/2Z x Z/2Z induced by rational Diophantine triples (Glas. Mat. 55 (2020), sec 3).

last edited by hdeping at 2026-09-27 08:25:27 UTC · history