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curve #552

y² + y = x³ − 13073767x − 11170229244

a-invariants: [0, 0, 1, -13073767, -11170229244]
rank (lower bound): ≥ 11
torsion subgroup: trivial
conductor (N): 89112822238948771487557
discriminant (Δ): 89112822238948771487557
Faltings height: 3.1044
naive height: 60.7720 ★ record for rank ≥ 11
primes of bad reduction: 1201, 74198852821772499157
regulator: 14610814.2772642708432326831778851025549951533983405773059318
submitted by: NDElkies
submitted at: 2026-09-03 13:56:30 UTC
last updated: 2026-09-03 13:56:30 UTC

Witness: 11 independent points log in to add more points →

(-916, 6063)
(-937, 16038)
(-957, 21561)
(-968, 24044)
(-974, 25290)
(-1023, 33669)
(-1051, 37541)
(-1114, 44849)
(-1125, 45977)
(-1297, 60038)
(-1359, 63930)

Commentary

Found in the output of the searches from earlier this year that found Curves 157, 158, 244 of ranks 12, 13, 14 and smallest conductor known.

last edited by NDElkies at 2026-09-03 13:56:30 UTC · history

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