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curve #4338

y² = x³ − 6700149x + 1247009956389

a-invariants: [0, 0, 0, -6700149, 1247009956389]
c-invariants: [321607152, -1077416602320096]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/3ℤ
conductor (N): 134675386853436
discriminant (Δ): -671755365019742055011037936
Faltings height: 3.8266
naive height: 69.2267
primes of bad reduction: 2, 3, 11, 13, 19, 137, 487, 2293
regulator: 1492.7031343634208175907023431736873924102918611792
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:05:24 UTC
last updated: 2026-10-17 10:05:24 UTC

Witness: 6 independent points log in to add more points →

(-8148, 872157)
(-10409, 434701)
(-5340, 1063257)
(16305, 2339337)
(101529/4, 33399093/8)
(-8889, -777309)

Commentary

BASE torsion/torsion_Z3.tsv.gz:567 (mrubinst/elliptic-curves-by-rank) + conductor prime factorization via pCwOrM Werr 4-Pillar Algebraic Sieve.

last edited by Volkan Dagli at 2026-10-17 10:05:24 UTC · history

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