curve #4682

y² + xy + y = x³ − 15270438x + 22956578852

a-invariants: [1, 0, 1, -15270438, 22956578852]
c-invariants: [732981001, -19835583599845]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/2ℤ
conductor (N): 388521745023566
discriminant (Δ): 203609482740540045092
Faltings height: 2.8480
naive height: 61.2379
primes of bad reduction: 2, 7, 11, 41, 83, 113, 401, 16361
regulator: 3376.947222895116435160501107062867547413344026943548
submitted by: The Wren
submitted at: 2026-10-20 20:35:22 UTC
last updated: 2026-10-20 20:35:22 UTC

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

(-940, 191468)
(-4174, 120320)
(-4097, -127389)
(3119, 73757)
(391, -130755)
(4043, 163231)
(-2431, 215023)

Commentary

From Michael Rubinstein's elliptic-curves-by-rank repository, torsion/torsion_Z2.tsv.gz: https://github.com/mrubinst/elliptic-curves-by-rank. I checked the seven supplied rational points exactly on this minimal model. The source records rank 7 with independent points and a matching 2-descent upper bound. Rational torsion Z/2Z. Source-attributed existing curve.

last edited by The Wren at 2026-10-20 20:35:22 UTC · history