curve #5674

y² = x³ + 13863018203x

a-invariants: [0, 0, 0, 13863018203, 0]
c-invariants: [-665424873744, 0]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 6149864758294699174688
discriminant (Δ): -170511374180455219794217641691328 ☆ record for quartic twists, rank ≥ 8
Faltings height: 4.8742 ☆ record for quartic twists, rank ≥ 8
naive height: 81.6711 ☆ record for quartic twists, rank ≥ 8
primes of bad reduction: 2, 17, 19, 157, 461, 593
regulator: 2505937.87000809512904128761930166145265784233670748720
submitted by: Michael Rubinstein
submitted at: 2026-10-24 04:21:24 UTC
last updated: 2026-10-24 04:21:24 UTC

(78831, 39783378)
(24021, 18624282)
(2264893/9, -3763186334/27)
(16284825/4, 65744009835/8)
(5500652/121, 35817495498/1331)
(30071623/441, 329043698866/9261)
(405612, -268988358)
(1768919/121, -19093711686/1331)

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 2026-10-24 04:21:24 UTC · history