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curve #4038

y² + xy + y = x³ − 6613x − 95028

a-invariants: [1, 0, 1, -6613, -95028]
c-invariants: [317401, 81627875]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/2ℤ
conductor (N): 1568718634
discriminant (Δ): 14648694604292
Faltings height: 1.2212
naive height: 38.0038
primes of bad reduction: 2, 7, 23, 29, 103, 233
regulator: 65.2858310378620456192986539741088875094585406450
submitted by: NDElkies
submitted at: 2026-10-06 19:05:48 UTC
last updated: 2026-10-06 19:05:48 UTC

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

(88, 36)
(-27, 266)
(249, 3578)
(-50, 358)
(111, 680)

Commentary

3rd-smallest naïve height for this MW group, by exhaustive search

last edited by NDElkies at 2026-10-06 19:05:48 UTC · history

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