curve #1379

y² = x³ − x² − 97601524740238182168191361387491320305220423747377441x − 3518287165082200027561400013604098557482789808182196013018931231782963307170495

a-invariants: [0, -1, 0, -97601524740238182168191361387491320305220423747377441, -3518287165082200027561400013604098557482789808182196013018931231782963307170495]
rank (lower bound): ≥ 13
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 14545260576720879419495082714314736176851942086001467334920374959680
discriminant (Δ): 54157051118179130527736222739761783293061542708942220779193282013833702442568863224692098719145235621645054138628319435028226712175831278442044594117961359360000
Faltings height: 29.5335
naive height: 377.6518
primes of bad reduction: 2, 3, 5, 7, 13, 17, 19, 23, 31, 37, 43, 47, 53, 59, 61, 617, 1117, 1277, 2309, 6173, 8521, 9811, 29753, 123953, 138433, 94669559
regulator: 24244457340333466466809.30021283425902878900891007528826689311457
submitted by: jesper-petersen
submitted at: 2026-09-24 19:11:33 UTC
last updated: 2026-09-24 19:11:33 UTC

Witness: 13 independent points log in to add more points →

(63996513289110046994410704592435663881/22755119104, -508748927894805897539914008878884820541747394626725223909/3432564206600192)
(23383414360373338107390906074184698461/48778256164, -83349469063302852829462519210596263228410674672436589319/10773068099868712)
(-45540455300446384515602760687/256, 11739704608435474787688287455022316121484025/4096)
(-118398332881652495834200290367110029554523/463541675080324, 21745411748547054554406051071469858855169213980146671812889875/9980060608229527165832)
(65827299195320580571642185155641757657407514264507546716369/178094078605383224838048669552400, -7848011296843765164932590672673357240830384119925263156372494402803989336231874870792497/2376699199888409693780028721727012766692256232000)
(9263201683455194850504487899541363779597060961489/1746017985421513441936, -28143768677441788894771152083878090828966829270753229081781891262465086833/72958025084497190704950287125184)
(3786492031119961168925327368332680335265215664497016929/3765048822777954990638223616, 6990157241485356566286331758540068665536587331324517181378813724839337040417641873/231023371920486669121230170688660925681664)
(9983610142661677060700635773690280920990956272490784973789/10970873006342981084351318628100, -934432793930775596327101108554468424965837788876394363440002165841977190661243723140937/36338063696209177275161711182559955253949429000)
(28344176867652682821089242581843974060085233679500547229921/48782451571798052919039740928400, -3972366999522977420182927076206783231552964406671689253799501285480179380808108608496919/340718278775168930795554701604580558868178952000)
(10788559734768684928380892815764494907056441/7651172342160400, -34532525341906542174883784825894974739060058283293458704241217189/669255542917665505192000)
(-19207326906323176003206145888162255674811881691023/492354474131017107356224, 165645545492761958324987655593965649647937666962226033155629696496092904425/345475165221626947743461757940602368)
(-108222337138751910390962655195477995060020572416305523/373342748396538473984373849, 4656317182751804040449631605325950759188357083400803172007407117425719817516800/7213758189835125004852930368874149926493)
(64887350462370885994670274771783841568752810245887199280912408441631536556701/2408665923357544321728690772935893009619320508900, -16527638925702452814162935415120510325725029320088315616682497469841450000526721164355727726185973978177513968699399/3738219965926677578662969463476632515057170966612179787776351054366063000)

Commentary

Obtained from ICARM curve #803, a rank-at-least-13 curve with torsion \(\mathbf Z/4\mathbf Z\), by quotienting by its unique rational point of order 2. The resulting 2-isogenous curve has global minimal model with ainvs \([0,-1,0,-97601524740238182168191361387491320305220423747377441,-3518287165082200027561400013604098557482789808182196013018931231782963307170495]\), torsion \(\mathbf Z/2\mathbf Z\times\mathbf Z/2\mathbf Z\), and the same conductor \(14545260576720879419495082714314736176851942086001467334920374959680\). The thirteen independent source points were mapped through the isogeny to thirteen independent points on the quotient. The isogeny, minimal model, conductor, torsion and mapped points were verified in Magma.

last edited by jesper-petersen at 2026-09-24 19:11:33 UTC · history