curve #4082

y² + xy = x³ − 140460326502749537468565820238840415795613381190766x + 382221153691490936882422487330355584819895511609003596409440087111653297796

a-invariants: [1, 0, 0, -140460326502749537468565820238840415795613381190766, 382221153691490936882422487330355584819895511609003596409440087111653297796]
c-invariants: [6742095672131977798491159371464339958189442297156769, -330239076789448169466413039166570733482356419766918164494266172548631895030897]
rank (lower bound): ≥ 20
torsion subgroup: ℤ/2ℤ
conductor (N): 428610428388219248912417769724228361243960259613932319147782453962458759457805385527477270
discriminant (Δ): 114241822360835408022497488127981153328766853453112544693298950039520879355932126845633749815303489485454500529255910159684390248628331209573420111360000
Faltings height: 27.8770
naive height: 358.0206
primes of bad reduction: 2, 3, 5, 13, 23, 37, 53, 61, 71, 79, 109, 137, 263, 317, 367, 661, 1109, 1237, 2141, 3253, 3881, 8011, 11027, 12781, 15731, 17483, 28001, 39023, 894227, 22707917
regulator: 229676653253281008959036.074647951944341475534026264752044499123880521083225094
submitted by: wgxli
submitted at: 2026-10-09 05:46:51 UTC
last updated: 2026-10-09 05:46:51 UTC

(2641597131823941957374076, 5441940497955440906986568215656732162)
(466905985240466097274326, 17797223733581213243795627916348128262)
(10437960597139236520241376, 7302620685206335646070623599504886562)
(-12984978709037778813697924, 4086869312000917899601620049435877762)
(-13027546053772403413177020, 1038779645440061360583420771133306914)
(13384735110081775722929154, 30001456011267245049298735880795787078)
(14021144082168661116485976, 34194417450345061734083845152467397762)
(-11471553834300448260490974, 21997783369037616526786552947786718662)
(-11931248349223783259300724, 18963624814300308603408867560931810162)
(25221665109215306309139420, 113507250717478750062017929586557392066)
(32205880609571134538071026, 171064653691004134205440187169715597062)
(53355120655471559117048220, 380496572431457095308693628780162831266)
(252203790183721853970237954, 4000852593559881395170775500392342349638)
(2239891075446620610855095526, 106006934804287963526340379607969513662662)
(29521433222654541478565973/16, 727859285683062603458635464642132821133/64)
(29853403925373464725832101404, 5158111804922473329282691643686612591542978)
(28094262075171197204844686844/169, 4697189704339374532830721381304076253063914/2197)
(3661046976142816018324918044/1369, 256888313800372755145649475360876056054586/50653)
(14663550946762874316655034700/1369, 522988767653815141667883938442806437260858/50653)
(-9927826461265172698413384804/1849, 2490994928154364512103743298236080109376806/79507)

2-isogenous to curve #4078

last edited by wgxli at 2026-10-09 05:46:51 UTC · history