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curve #4097

y² = x³ − x² − 935215007281x + 35046690582446881

a-invariants: [0, -1, 0, -935215007281, 35046690582446881]
c-invariants: [44890320349504, -30280071321312008192]
rank (lower bound): ≥ 10
torsion subgroup: ℤ/2ℤ
conductor (N): 1739383412924152840357920
discriminant (Δ): 51819118104214037561190252036746342400
Faltings height: 5.9264
naive height: 94.3057
primes of bad reduction: 2, 3, 5, 11, 23, 31, 43, 139, 331, 6121, 1230769
regulator: 3194901.024318785319920550356114493876631299061424865505473
submitted by: Michael Rubinstein
submitted at: 2026-10-09 14:51:02 UTC
last updated: 2026-10-09 14:51:02 UTC

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(-974667, 143732116)
(1092541, 563375340)
(-8147, 206555916)
(-436459, 600071340)
(-799899, 520881460)
(-129955, 392922156)
(4316368, 8741663991)
(12736015, -45320889396)
(2217885, 2978363564)
(3074125, 5119697484)

Commentary

Torsion Z/2. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-10-09 14:51:02 UTC · history

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