curve #6160

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y² = x³ − 29568291643277670150527990336731492x + 2032673876319662548364241285902491862216947427571076

a-invariants

[0, 0, 0, -29568291643277670150527990336731492, 2032673876319662548364241285902491862216947427571076]

c-invariants

[1419277998877328167225343536163111616, -1756230229140188441786704471019752968955442577421409664]

rank (lower bound)

≥ 24

torsion subgroup

trivial

conductor (N)

115095099937310703106659129718708004058942223594963625903587662089546222718527924681644846120

discriminant (Δ)

-130452503840675926036797802713073566068936220056353890924242942093777181172173358286143485720937676000000

Faltings height

18.7418

naive height

249.8055

primes of bad reduction

2, 5, 7, 11, 13, 67, 13241, 98867, 1065350999036085143277491773457393747, 30762604612820571914297711817434741987251

regulator

37208772026210545782826609.860750951798727992369225073715112843644715190591227749365410

submitted by

apkorte

submitted at

2026-10-29 20:37:34 UTC

later contributions

primes of bad reduction recorded · Daniel Błażewicz · 2026-10-29 20:41:50 UTC

Witness: 24 independent points log in to add more points →

(402484040899014593/4, 69847258683591797941357825/8)
(646071976353466042, 502598931504124436400569150)
(157212717084262362, -35634344661659904079320830)
(105387475076429640, -9329221145028345348301514)
(700794666451677393/4, -377782738004425693971487225/8)
(527052967757782985/4, 164783354054843295860251163/8)
(3601437186983960665, -6826964513542673464502502211)
(158219720270489530, -36265372299835228573468354)
(195225873438729385898/1849, 744934428061780806907384114970/79507)
(15800999048970242, -39615784586949972513780850)
(-269458057013132807/4, -487857606195083658185478125/8)
(1015936668099041248/9, 311760794020341596413936310/27)
(299176279633824232, -141296666603636339584125610)
(88077229245843217, -10566382528419576265832425)
(247855977765244657, 99651541076941058073111815)
(50989173611562566, 25643277090618734177620990)
(228166657443930653978/2209, 931789430747144482977089976350/103823)
(349355853947382073/4, -86325821075465842556625485/8)
(100429471137417230, -8722702053965417609608946)
(527499631647919908337/63001, -668227121664552576627584991871145/15813251)
(-1002697222076041922/9, 1695640675449243405936249350/27)
(20005172198081177, 38067851510634821473330915)
(101232573195618832, -8765527235477410678105490)
(86907836710119966, 10925661478149818380442350)

Commentary

Specialization at T = -287/2 of the rank-17 fibration of X1092 given in curve#1675. 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 2026-10-29 20:37:34 UTC · history