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curve #1671

y² = x³ − 23710129369092x + 18108316143621428401

a-invariants: [0, 0, 0, -23710129369092, 18108316143621428401]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/6ℤ
conductor (N): 51472046920140
discriminant (Δ): 711406654441979367106135324398545975250000
Faltings height: 6.7243
naive height: 104.0044
primes of bad reduction: 2, 3, 5, 7, 11, 19, 29, 41, 43, 3823
regulator: 661.166703000784852255090058760797641819118323195
submitted by: Michael Rubinstein
submitted at: 2026-09-25 02:54:19 UTC
last updated: 2026-09-25 02:54:19 UTC

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

(8198342, 19358672025)
(-18413372/9, 205720988075/27)
(-1156207/4, -39950064825/8)
(-1323793, -6868461810)
(-2755570182/529, 6369216324625/12167)

Commentary

Torsion Z/6. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-25 02:54:19 UTC · history

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