curve #747

y² = x³ − x² − 9008852820377383610174292043276433x + 355962798443136049924872453718086113933860870626837

a-invariants: [0, -1, 0, -9008852820377383610174292043276433, 355962798443136049924872453718086113933860870626837]
rank (lower bound): ≥ 23
torsion subgroup: trivial
conductor (N): 7984751558079104972746782605220711236089923859646184489024403069751133842847257245758600
naive height: 246.3210
Faltings height: 18.4855
discriminant (Δ): -7944695459732437794258110307402026108921956919186644034086453498110776104724727287158376831845617120000
primes of bad reduction: 2, 3, 5, 7, 29, 31, 37, 179, 319299082519787340784137635167614330086839330734305269554690287558269650592729
regulator: 1286297487816386348465066.97909869307465905933163265860626281918944099574451945938596
submitted by: Valery Asiryan
submitted at: 2026-09-16 18:18:25 UTC
last updated: 2026-09-16 18:18:25 UTC

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

(-105652498745225204, -11332688261765523757302667)
(-112594212876235333059/1156, -691368183348862264732081445913/39304)
(-89379357041858719, -21145830104118905588197662)
(-88832627114312483, -21336439925194675774211110)
(-18099196062247541387/5476, -7958321041277925150139583318581/405224)
(19358476067535833, -13741169424806446710423714)
(43944912659539441, -6703282868687028253698782)
(51732721016935567, -5325531610642952586102890)
(54385118623382981, -5183856791272161513065562)
(59230032692925753, -5491699273711842605114334)
(4862091075633258457/81, -4090072609930847120451493010/729)
(64598371354223487, -6600857913383360634079590)
(69327461585073717, -8038051155726627072252390)
(74816558509246457, -10036853311789776331911390)
(19236333393702502457841113/191462569, -57129637060086314248905021399682128330/2649267567253)
(195795355353649690035833/923521, -79258735128673286134461149166123426/887503681)
(449372309716068757, -295045494114446425533331610)
(1429164186649133045620993/1108809, -1704035906006108572907176519764547030/1167575877)
(1368884612047286177, -1597842789412810878908367390)
(1659703404809362511, -2134771295486976674218360278)
(28627737110604222417/16, -152961499763686917114117614385/64)
(3821931069398266388, -7469502814875966528861791769)
(7724069905544843652, -21465285514579307736337043265)

Commentary

Specialization T=-43/75 of the family identified by wgxli in the commentary to curve #302. The points were obtained by specializing reconstructed generic sections and running minimized quartic searches. The 23 listed points are certified independent by exact quadratic-character certificates.

last edited by Valery Asiryan at 2026-09-16 18:18:25 UTC · history