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curve #1256

y² + y = x³ − x² − 50905670355791670x + 4420764579970944391090872

a-invariants: [0, -1, 1, -50905670355791670, 4420764579970944391090872]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/5ℤ
conductor (N): 24491520312771563
discriminant (Δ): -1220269318349108529747840814966737170656926683
Faltings height: 8.0939
naive height: 127.0199
primes of bad reduction: 193, 199, 389, 1151, 1424231
regulator: 24401.49715192084355416771587503607810962491860
submitted by: hdeping
submitted at: 2026-09-24 16:29:40 UTC
last updated: 2026-09-24 16:29:40 UTC

Witness: 4 independent points log in to add more points →

(506689981/4, 565297001347/8)
(157808613554020/1207801, 10380926056793881392/1327373299)
(10496514177192804724/28167244561, 28832806443045833941360116240/4727336821917191)
(2820850144966927/1580049, 148677490644401086343900/1986121593)

Commentary

Found by a Mestre-Nagao sieve over the Tate normal form family y^2+(t+1)xy+ty=x^3+tx^2 with torsion Z/5Z, at t=38407/389.

last edited by hdeping at 2026-09-27 08:30:30 UTC · history

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