curve #3561

y² + xy + y = x³ − 2750616591267822630875308500917209370505942528x + 53391440442331869351542555861281639389498006827932006992596173091722

a-invariants: [1, 0, 1, -2750616591267822630875308500917209370505942528, 53391440442331869351542555861281639389498006827932006992596173091722]
rank (lower bound): ≥ 28
torsion subgroup: trivial
conductor (N): 3502614076072580792087513486617482680169106763841684533585471138569582383808955049470281611352240218219113035290098900822082
discriminant (Δ): 100416457070396468797237984335386267586898538647340708102215799574204723396834612745063445023191926696976007366241887744734203280253297812
Faltings height: 25.0516
naive height: 325.4981
primes of bad reduction: 2, 3, 13, 17, 31, 37, 257, 557, 439903293497, 2151250049398117010447817201021895484894618036247659991371598289901529074102265621549798270946284881
regulator: 4758585713706160958880414319975163062059.972650078266617497066628216620198371317565616538853419
submitted by: Matej Jurasić
submitted at: 2026-09-28 14:38:24 UTC
last updated: 2026-09-28 14:38:24 UTC

Witness: 28 independent points log in to add more points →

(23629714833183079589324, -1260604313952646924925971518165282)
(20382863717623277956805, -2407132107673911525347925083805807)
(-55457750298090028407163, 5947326737838242033919699510730521)
(-47082892719725091415675, 8861440450609390555346604798033441)
(51588024857425672520156, -6984627975025601992329757669237467)
(11792035753243880600276, 4753501727601907991691266885047485)
(23918044428464441389154, -1133549483784839000732210440864797)
(24945492304613572481663, -546787136643768403987169596619709)
(-2885899532868931154452645/49, 1142638583886741108737875551855772239/343)
(19813642251132490100423, -2582664382940251365611575461851229)
(-20995988658623233722451, -10093941806231195536337259123244707)
(112271628290112828232415, -34055101872190993441981705525871037)
(41517029125056570624119, 3279543817573108813873645286970597)
(-58804942517018597929492, 3434028145046248302162453314208501)
(211315794724045619151367/9, 35740530539619709024396375291885457/27)
(4922527691240294287604957/49, 9646298959410584369499476399651224875/343)
(29549389855076986435609205/784, -39644699465767191374481187909460228013/21952)
(17586806612471349653697747355073778056/500384821934089, 4075921167390762977359509912725519196654605516142291186/11193249690748244188187)
(77912054727784567844259540588185485384/2185067632515849, 82179979958187054720480284800182959201850770892984540955/102140346257137034361243)
(-1246400111509115904106902217896735430036/49228841781790225, 112881128560267498552505709638053915094737711256530664337267/10922685453533415787690375)
(617188821103554056152593686478740323598306/180145029328112209, -484815475165442337062280555663257740722420108774210855381671349/76459847056060927005641177)
(410901413123547514158927919467638986348583/64777149169710916, -263385373113743619952171985566839497380758504609967744923688395/16486662453171274383755464)
(133767328517200355518281966064878389610163907/191591800511777634049, -1542874418765389352050855832369678103457138286024423189848626509775/2651950284456914008526944342657)
(4152317259672482764297386915442433737184269/86361786471264603049, 4560523476501441900833528416175228652529620242095782352679443931/802569084289169080170372636907)
(764402931416732505205983781131759585007020935/4650160108322061342916, -20163142311308551911890270538538248657076704412927153206672562216029/317104101493798297816797350052536)
(554296443357173682712383827318634514956882233/29688108598846302784, -13050027482644304578368705015809394419247374922940146808046709236553/161760989547574614397670205952)
(1615416760613663930626838515736195162796932991931/1426107238844400962811025, -2051015162958915487047448125449907551746682410752766725450680532172049281/1703053442510842266715683620357842375)
(12647694683494101827382548145358654533049265253559550/579870101080026790051326508729, 857745226212623587378688380931735199341423440458240445410174588201196832676861/441566456343844500423741515224318539254250067)

Commentary

Specialization at T = 13601/15 of a rank-17 fibration of X1008 (2-neighbour of the one in curve#751).

last edited by Matej Jurasić at 2026-09-28 14:38:24 UTC · history