curve #4071

y² + xy + y = x³ − 10280592017918005843861895426451801689170145912391885663x + 12668424643103352460599031639440218482617698012419233943498230308244436216485983992

a-invariants: [1, 0, 1, -10280592017918005843861895426451801689170145912391885663, 12668424643103352460599031639440218482617698012419233943498230308244436216485983992]
c-invariants: [493468416860064280505370980469686481080167003794810511801, -10945518891641296525957563337216551394271787503488274597887000707943443396736105937005]
rank (lower bound): ≥ 20
torsion subgroup: ℤ/2ℤ
conductor (N): 6131429525853961023265331906599034669054966945113256585858859273406727832034414573630186014
discriminant (Δ): 208705183794499293693464517227770609663745397051032065153666015263841299818622357747325434410786747627987316944441503604344127948701082890363412271302714151858942642
Faltings height: 30.4238
naive height: 391.6232
primes of bad reduction: 2, 3, 7, 11, 13, 17, 19, 31, 47, 61, 71, 73, 97, 101, 151, 157, 163, 211, 317, 331, 337, 409, 431, 521, 541, 739, 761, 1637, 3433, 6397, 22037, 81157, 472859, 2737040129
regulator: 466951759389483601197723.008378158435093244671519404332634057473562706210491170
submitted by: wgxli
submitted at: 2026-10-09 03:55:25 UTC
last updated: 2026-10-09 03:55:25 UTC

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

(1722679356686241331402321412, 8397969302930543617610141841084540503871)
(1912383560862817093982568662, 1406927503014170213573996119024715314491)
(1946731582670994199008304400, 5703022058488329618744603078738062781768)
(1964734062154511874229484120, 7349988483434448623105040833179531034583)
(818533322855968670384586176, 69295253843746686314833832743999498437240)
(1323465348692073994471705808, 37155713017871220661732345344898369998600)
(2093580684297061353063545900, 17930632112278112576131478681029387686831)
(2818565413080722925731115028, 77996562337182097609075437513571934502476)
(2841040935220622081097499100, 79952125776510777059820069076642697155668)
(3471071406904514774008704080, 137129109618812434108774009750459761070728)
(6030893490927931554606209504, 412335997706517402256805745069965692646808)
(-2695868450368183698937453100, 144190038184678007643659377483368283026956)
(11119346210352292396090348766, 1128339210126008515877016201945600930077718)
(90350941651829921477113283180, 27141204575850102670655189506372596704256303)
(388934510220145418203664479514, 242549290370740371796426085037270225823862082)
(21564465553826671863650761714/9, 1142798854208208526254434254341547076392430/27)
(30682589598423193922877447445/16, 153958823497755373973251887484731225153887/64)
(43897707951926105218266537196/25, 690207745384716153722656220515166118646579/125)
(1775535131210360457418029139879/1156, 880214839011716457143602897412966391666223397/39304)
(16392464876943688698679236657578/3721, 52193763536003222980896119742940739652349620810/226981)

Commentary

2-isogenous to curve #4070

last edited by wgxli at 2026-10-09 03:55:25 UTC · history