curve #4973

y² = x³ − x² − 80147258683421384x + 8733351300954638705041968

a-invariants: [0, -1, 0, -80147258683421384, 8733351300954638705041968]
c-invariants: [3847068416804226448, -7545615500942397340330901696]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/4ℤ
conductor (N): 16595433408864784656
discriminant (Δ): 29382965618963591022620769572745503913071726592
Faltings height: 8.2482
naive height: 128.3815
primes of bad reduction: 2, 3, 7, 13, 23, 29, 31, 107, 127, 131, 233, 443
regulator: 69430.17658945720600136394469310958328254451327023255
submitted by: The Wren
submitted at: 2026-10-21 00:48:01 UTC
last updated: 2026-10-21 00:48:01 UTC

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

(-86895172, 3878354752272)
(110288066, 1111552669542)
(130612716, 702361369008)
(166292924, 63114762480)
(187764733, 551615819638)
(1483294228/9, 813059761384/27)
(3933420764/25, 16812245228688/125)

Commentary

From Michael Rubinstein's elliptic-curves-by-rank repository, families/family_Z4.part2.tsv.gz: https://github.com/mrubinst/elliptic-curves-by-rank. Seven rational points checked exactly; PARI/GP returned rank bounds [7,7]. Rational torsion C4. Source-attributed existing curve.

last edited by The Wren at 2026-10-21 00:48:02 UTC · history