curve #4655

y² + xy = x³ + x² − 234335842x + 1241980996480

a-invariants: [1, 1, 0, -234335842, 1241980996480]
c-invariants: [11248120441, -1073155941861965]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/2ℤ
conductor (N): 476466991732661082
discriminant (Δ): 157089654868026599269125732
Faltings height: 3.7599
naive height: 69.4304
primes of bad reduction: 2, 3, 41, 61, 73, 113, 127, 173, 4273
regulator: 35746.8330293536570689043870110681453632778280394761206
submitted by: The Wren
submitted at: 2026-10-20 17:40:09 UTC
last updated: 2026-10-20 17:40:09 UTC

Witness: 8 independent points log in to add more points →

(-3974, 1454740)
(-1307, 1244047)
(3939, 614527)
(1438, 952162)
(-653, 1181311)
(-214587/16, 90317615/64)
(5056, 429280)
(-14134, 1322660)

Commentary

From Michael Rubinstein's elliptic-curves-by-rank repository, torsion/torsion_Z2.tsv.gz: https://github.com/mrubinst/elliptic-curves-by-rank. Eight supplied rational points checked exactly on the displayed model. Rational torsion Z/2Z. Source-attributed existing curve.

last edited by The Wren at 2026-10-20 17:40:09 UTC · history