curve #4080

y² + xy + y = x³ − x² − 3634658042725195230582852262491019833776027829466292x + 84339127251430364070582089347348202634634278628523834299900771792496735924759

a-invariants: [1, -1, 1, -3634658042725195230582852262491019833776027829466292, 84339127251430364070582089347348202634634278628523834299900771792496735924759]
c-invariants: [174463586050809371067976908599568952021249335814382001, -72869005945235834556982924411022709847681846929148504137053982733095168674273001]
rank (lower bound): ≥ 20
torsion subgroup: ℤ/2ℤ
conductor (N): 59922190121336398795572364641929095928611712492963586620439649207478009865597394590
discriminant (Δ): 203038243143181014121555666509830546045097562931890750270019473541501147145856767912168499950146607900388664483105923429509835512257599212593061739200000
Faltings height: 28.3105
naive height: 367.7807
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 19, 29, 31, 79, 89, 103, 151, 167, 229, 263, 283, 307, 313, 479, 2381, 2621, 3919, 5431, 10459, 12101, 13441, 14851, 16481, 35509, 260111
regulator: 11065372938594331175952.4158576786254974221229195889762077803801054439529188667
submitted by: wgxli
submitted at: 2026-10-09 05:33:33 UTC
last updated: 2026-10-09 05:33:33 UTC

Witness: 20 independent points log in to add more points →

(34971286460911245808590717, 154729044975266855471147686651020541)
(34196560122541048761156117, 5995325486372133825156469389752675341)
(35006313879760928127708489, 1163897074873419998698772075241989893)
(35053379526004221981116007, 1883753421423568979855323428454414891)
(35349075963818948604976269, 5292955032213304133418661693814993437)
(35399231688286311696387117, 5831011874114138502594941818947989341)
(35417026269960020748147267, 6021011789094200261623321228616138791)
(28677291106491052437039117, 60752058497595093755168890393336877341)
(33206830355627881062223317, 16143510972851627258915944216104096541)
(33469444244003343557058567, 13481014673976875135395392720691714891)
(35807548207359048721113717, 10132844729539264259149145861648310541)
(37216684415109489117490867, 24846542459775978225100179696501704791)
(42990936530756100720730749, 86824590744099490538676787969259610757)
(8390757197249228765352879, 233307401844513362495774728302007026493)
(9506478972711680206012437, 225045456238832805154014952337468740621)
(-56592078567553738777388331, 329828143841043751061325721750673259037)
(939149044620571829000714541/25, 3563800567211418061880547966578509125449/125)
(-2361045504836743437304595667/49, 131776651891824986233711252607485407627763/343)
(28284755661422637348099046597/841, 288345094171822379934013258040238741523449/24389)
(1083113612330487929330211528673/33489, 152194639450645286681351079837170791458620687/6128487)

Commentary

2-isogenous to curve #4079

last edited by wgxli at 2026-10-09 05:33:33 UTC · history