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curve #4053

y² + xy = x³ − 65429458282822x + 203698297643610081636

a-invariants: [1, 0, 0, -65429458282822, 203698297643610081636]
c-invariants: [3140613997575457, -175995333875000106896689]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/3ℤ
conductor (N): 13047414767043566
discriminant (Δ): 1707938204811166123135801474391289626624
Faltings height: 6.5938
naive height: 107.0496
primes of bad reduction: 2, 7, 13, 19, 31, 37, 43, 97, 103
regulator: 7039.893953051426596738068499939524216570435190404977
submitted by: Michael Rubinstein
submitted at: 2026-10-07 22:25:04 UTC
last updated: 2026-10-07 22:25:04 UTC

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

(4714412, -136128662)
(41229964/9, 8499528238/27)
(-1653460, -17530940054)
(6403372, 6873404778)
(-1024015924/121, 16377281123870/1331)
(4962436, -1103670286)
(-8130932/9, -437081279954/27)

Commentary

Torsion Z/3. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-10-07 22:25:04 UTC · history

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