curve #1995

y² + xy + y = x³ − 53418633100034896795079654x − 148088983872327184564679098211137496394

a-invariants: [1, 0, 1, -53418633100034896795079654, -148088983872327184564679098211137496394]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/6ℤ
conductor (N): 4688824384798005181241330 ☆ record for ℤ/6ℤ torsion, rank ≥ 8
discriminant (Δ): 281786663080052415882993009512474133787635435016782306148013704662610780627850
Faltings height: 13.6596
naive height: 189.3342
primes of bad reduction: 2, 5, 7, 13, 19, 29, 47, 67, 73, 139, 379, 421, 719, 2551
regulator: 9074742.91844786475147596172385118190296768466372118493
submitted by: Steps Unbounded
submitted at: 2026-09-26 04:31:19 UTC
last updated: 2026-09-26 04:31:19 UTC

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

(-331404997446950/81, -1025757108288030841622/729)
(-7864827491888248/1849, 117166765155085942186166/79507)
(1410363253578314, -52965202713299962012358)
(-493206794094406/121, -1848090999290303363698/1331)
(-14973862795291225/3844, -224647848758063964574169/238328)
(-9704458577314301325/2540836, 1905695333313256854277478763/4050092584)
(-1663675728130899/400, -11702996628316382891309/8000)
(-341987189115685351507108/89572708369, 12218865948456085241518501707997879/26807947169632903)

Commentary

New curve, 2-isogenous partner of curve#1913; the 8 witness points are transported through the rational isogeny and certified independent by the exact 2-descent character test.

last edited by Steps Unbounded at 2026-09-26 04:31:19 UTC · history