curve #5536

y² = x³ − 13364091988266573174378318086587x + 18947727543297532356328893414701065738198420666

a-invariants: [0, 0, 0, -13364091988266573174378318086587, 18947727543297532356328893414701065738198420666]
c-invariants: [641476415436795512370159268156176, -16370836597409067955868163910301720797803435455424]
rank (lower bound): ≥ 23
torsion subgroup: trivial
conductor (N): 19018992132020173517482799032285613650733072760724974507000367189177828784735120
discriminant (Δ): -2339052761087387978343594070064407733236180293095504895303740959959913263239160460954505600000
Faltings height: 16.7397
naive height: 226.6392
primes of bad reduction: 2, 5, 7, 13, 29, 31, 59, 18492973, 529774253, 5027439264858175154535431253786125213008522759397531351
regulator: 181714862590987239004667.192048744646080951568969538814242703416163635461405526092316
submitted by: apkorte
submitted at: 2026-10-22 23:29:11 UTC
last updated: 2026-10-22 23:29:11 UTC

Witness: 23 independent points log in to add more points →

(2376290775299302, -24679903113981766272700)
(8875386053031553/4, -118351600891913172805385/8)
(1029326111957862, 79260976001035234582540)
(-2661437118758053, 188848616893980384768470)
(67230794367055419/25, 6196046654456150443584178/125)
(-2253849847235723, -193956669319744425339700)
(4025824618193433/4, 645816007992416737164325/8)
(2068630157480297, -12430187636940436550320)
(108384751783151923/49, -4964160070192630765504150/343)
(2326787395312987, -21199366402718583736790)
(-8195838364262357/9, -4704709279194904308688450/27)
(1745608960139322, -30633026091649791461470)
(763131824154883403/289, 223568880442070793870572150/4913)
(2152622334897571, -12436609074991911749030)
(1570383866374587, -42821786125161050772310)
(6756465723817926677/2401, 7082748967109638216521849100/117649)
(-2786148434560045, 185887738485479614308634)
(17336983927940897/16, 4848449909569359822284465/64)
(1363704068395205, -57088756267085974223884)
(2007499044251497, 14479365189231049366480)
(2695437477223027, -50090311393854103230950)
(43917670155479014/25, 3733644382399876743817088/125)
(2050448051904677, 12888995677523904778700)

Commentary

Specialization at T = -58/23 of the rank-17 fibration of X1008 given in curve#3594. Found by Claude (Anthropic): a Mestre-Nagao sieve over the fibration, then a 2-covering point search seeded with its generic sections.

last edited by apkorte at 2026-10-22 23:29:11 UTC · history