curve #6032

y² = x³ − 5177237214515800849011338287x + 148437574363861287280769403187001149250290

a-invariants: [0, 0, 0, -5177237214515800849011338287, 148437574363861287280769403187001149250290]
c-invariants: [248507386296758440752544237776, -128250064250376152210584764353568992952250560]
rank (lower bound): ≥ 21
torsion subgroup: trivial
conductor (N): 10212414370950124838379458948202235823276715824958296988385360304738363048
discriminant (Δ): -637312762280484527356370666621879265840821821714320133997788111246658282840480753408
Faltings height: 14.8476
naive height: 203.1251
primes of bad reduction: 2, 7, 19, 71, 163, 181, 948862559, 5388459680707, 45525586073389, 148008663822918394680161869
regulator: 2268261938315035911248.8644377141930198161828808747167260142323149321004977320671
submitted by: apkorte
submitted at: 2026-10-28 14:17:14 UTC
last updated: 2026-10-28 14:17:14 UTC

Witness: 21 independent points log in to add more points →

(31530678981767, -128619817181290622768)
(206409289398998, -2806035126160113976184)
(53288776900345, -154508064009273029930)
(52489913452977, 145960881524727095582)
(50700623039021, 127581619259460320282)
(413533131013191, 8290092559270750589312)
(48865187330022, -110143186614592475932)
(136889225348582, -1415927341482198819932)
(34764790531569, -102315239464882833886)
(42788868848663, 72464105848602794984)
(-74643394251037, 344961284113203971984)
(-1198646066160767/16, 21782917786280757811649/64)
(7836510920021, -329161579793068339282)
(94269307425881/4, -1590243681661381592293/8)
(142291847428497/4, -770795133639351883553/8)
(1511277050911541, -58685756355433076920462)
(22488006135077, -208288864673720755582)
(233399623464253/9, -4800827360639573792486/27)
(436715856126908449/4624, 222763378430557324669005361/314432)
(43709918327978, 75174777989578199366)
(242461505451137/4, 1915525681457431726697/8)

Commentary

Specialization at T = -19/2 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 2026-10-28 14:17:14 UTC · history