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curve #4046

y² = x³ − x² − 81115984x + 106896707344

a-invariants: [0, -1, 0, -81115984, 106896707344]
c-invariants: [3893567248, -92335393741760]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 10436253744
discriminant (Δ): 29224613699129042601329664
Faltings height: 3.5795
naive height: 66.2478
primes of bad reduction: 2, 3, 7, 37, 47, 53, 337
regulator: 116.312221634392733705552660254486700033636351704
submitted by: Michael Rubinstein
submitted at: 2026-10-07 22:23:54 UTC
last updated: 2026-10-07 22:23:54 UTC

Witness: 5 independent points log in to add more points →

(15334, 1571094)
(-9180, 278992)
(-9530, 119658)
(-8256, 462364)
(-25947/4, 4800565/8)

Commentary

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

last edited by Michael Rubinstein at 2026-10-07 22:23:54 UTC · history

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