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curve #5533

y² = x³ + 15960909912948x

a-invariants: [0, 0, 0, 15960909912948, 0]
c-invariants: [-766123675821504, 0]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 467861607436623935607072
discriminant (Δ): -260227334341665388635601377680476807385088
Faltings height: 6.6363
naive height: 102.8171
primes of bad reduction: 2, 3, 7, 11, 13, 31, 61, 107, 199
regulator: 217236224.375908891060997456566673903719611611741765761
submitted by: Michael Rubinstein
submitted at: 2026-10-22 22:49:54 UTC
last updated: 2026-10-22 22:49:54 UTC

Witness: 8 independent points log in to add more points →

(597, 97614873)
(49132902, 345533063148)
(274134/289, 604516458924/4913)
(41585229/289, 7450368042411/4913)
(417240912/5041, 411464288433528/357911)
(1162840182/529, 82257125965812/12167)
(2037676221/1369, 263466004539843/50653)
(251928299844/25, 126449020000826172/125)

Commentary

Rank 8, proved: 8 independent points listed, matching the 2-descent upper bound. Torsion Z/2. Member of the family y^2 = x^3 + a x.

last edited by Michael Rubinstein at 2026-10-22 22:49:54 UTC · history

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