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curve #1663

y² + xy + y = x³ + x² − 121669781609590x + 521608633134542224755

a-invariants: [1, 1, 1, -121669781609590, 521608633134542224755]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/5ℤ
conductor (N): 53288164177430
discriminant (Δ): -2263517822302726032995989524077399244800000
Faltings height: 6.9411
naive height: 108.9300
primes of bad reduction: 2, 5, 7, 13, 17, 29, 6359, 18679
regulator: 552.782958215057760093635665497217534440339204776
submitted by: Michael Rubinstein
submitted at: 2026-09-25 02:40:19 UTC
last updated: 2026-09-25 02:40:19 UTC

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

(54147817/9, 73219351061/27)
(158630377/9, 1675656259861/27)
(41078761/9, 211433330965/27)
(8013773, 7820548943)
(272153313, 4485965145743)

Commentary

Torsion Z/5. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-25 02:40:19 UTC · history

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