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curve #46

y2 + y = x3 − 489468383913472842641289697078
a-invariants
[0, 0, 1, 0, -489468383913472842641289697078]
rank (lower bound)
≥ 16
conductor (N)
141972917837550720141347359033819641029697926227598433712323
naive height
150.2494
Faltings height
10.5784
discriminant (Δ)
-103498257103574474983042224735654518310649788219919258176283467
primes of bad reduction
3, 41, 1768630113508483622913422573
regulator
359787206510825092.8999100746454939974782593912647860402619044739747445
submitted by
David Renshaw
last updated
2026-07-01 22:37:39

Witness: 16 independent points

Commentary

Rank 16 Mordell curve from Noam D. Elkies, "Rank of an elliptic curve and 3-rank of a quadratic field via the Burgess bounds", ANTS XVI. This is the minimal model (8) for E_{-432D}, with D = 72513834653847828539450325493 = 41 * 1768630113508483622913422573: y^2 + y = x^3 - 489468383913472842641289697078. The 16 submitted points are the independent points Q_j in table (9); the paper gives conductor 27D^2 and discriminant -3^9 D^2.

last edited by David Renshaw at 2026-05-28 05:22:40 · history

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