curve #4538

y² = x³ − 70436294596590642188694221797874388x + 7458409292195787394677002837557973032775817115470112

a-invariants: [0, 0, 0, -70436294596590642188694221797874388, 7458409292195787394677002837557973032775817115470112]
c-invariants: [3380942140636350825057322646297970624, -6444065628457160309000930451650088700318305987766176768]
rank (lower bound): ≥ 25
torsion subgroup: trivial
conductor (N): 1191963315491190432085751627750499783297858091671506618051145852163885623757400944788000960
discriminant (Δ): -1666209865747154152325984641937021458936349153793744470703914712508026703555212798069673354689120828518400 ★ record for rank ≥ 25
Faltings height: 18.9560 ★ record for rank ≥ 25
naive height: 252.4055 ★ record for rank ≥ 25
primes of bad reduction: 2, 3, 5, 13, 19, 47, 59, 151, 1946163833, 44792906047, 31719983970349621, 482396092200779351546860319209109152165339
regulator: 64745271433027401841873593.37734584501567016857696315482542363735469745891942239433323469
submitted by: Matej Jurasić
submitted at: 2026-10-17 12:04:58 UTC
last updated: 2026-10-17 12:04:58 UTC

(102859634226280346, -36078019036226080991842440)
(1116248420215284056, 1148778176453139409857240600)
(173482043587226802, -21449846629021793833378112)
(2082648295996656964/9, -1608817136189522665371765020/27)
(-269363845528824999/4, 872560515366877514292129469/8)
(100685972561485466, -37244907494206136747061000)
(862512910267650212, -767042468833295478935753772)
(-240421434567427186, 102449267637756759478501368)
(6204025092671470808/49, -8188857521480097741699077736/343)
(-512283512923095151/4, -959286723827247967695750375/8)
(-96550326993906172, -115581217058455545425813820)
(1232374285197623793/4, 979867402460012519465673559/8)
(138078006853542746, 19111183411801549972875240)
(-242337865589930098, 101468514278128602720008712)
(71844462471357146, 52619253800074908033998040)
(281600988957875378, -99770681269098841482287040)
(63401615840360102, 56986787857912767683801088)
(685927927366815782, 530915532961066707483530592)
(-141397717473583078, 120792928350405409615011768)
(12869507614675265636/121, -45527456487914534703576587700/1331)
(11741093301264281194/9, -39458818787478739495604077400/27)
(62069671203968889386/361, -142344283655276093759035214040/6859)
(6288124731016666664/121, -83528349027167188961141374608/1331)
(45613201806245202353/1024, 2175871339964940905908038497001/32768)
(-4618275051699716693874/36481, -834587509112862053079446110724360/6967871)

Specialization at T = -63/151 of a rank-16 fibration of X1008 (2-neighbour of the one in curve#751).

last edited by Matej Jurasić at 2026-10-17 12:04:58 UTC · history