curve #1980

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y² + xy = x³ − 113404222515329597795345382666335x + 466735960029383627598782809478106041052114459225

a-invariants

[1, 0, 0, -113404222515329597795345382666335, 466735960029383627598782809478106041052114459225]

rank (lower bound)

≥ 22

torsion subgroup

trivial

conductor (N)

27807679266450741313158521622216713214213739551417679783190817736421952030

discriminant (Δ)

-767972573587340720081156396301261642137351170229672956303158090326875671198845018653651968000000

Faltings height

17.2482

naive height

233.0473

primes of bad reduction

2, 3, 5, 7, 11, 13, 19, 29, 1126169621992299321284604458759, 1492292672023628690314221805436697289

regulator

603904905365553384626.0695091463841205582830637038429905567938444638148856943841373

submitted by

Ritik Jain

submitted at

2026-09-25 23:05:52 UTC

later contributions

primes of bad reduction recorded · Daniel Błażewicz · 2026-09-25 23:17:36 UTC

Witness: 22 independent points log in to add more points →

(88871814300982970062/14641, 79635304351630917176766314821/1771561)
(8357362544615415224396182500528310/1411371625887187129, 89445533493804842295156862291718504217720981687095/1676725901571872499576748883)
(1909150486429914971170/534361, -127878195498398477570211991520785/390617891)
(32255697588250044214/7225, -136538219254245967797959686007/614125)
(26923683564559966, 4114613434897077129739357)
(6838990652627590, 105059020065620513585965)
(6059745538714450, -45301344560612211197015)
(927477821295550150, 893154925610714800209358285)
(-8539930790354780, -901320943135594922410835)
(5750083832772190, 69064198128162180971845)
(4451481948779140, -223893512139072404412785)
(6550741199984620, 70434584383566486940765)
(3105785812142470, -380111631452929456186835)
(6181648761238555105/1024, -1514545703281770239230197055/32768)
(20967297637560236670/3721, -18489145770998674547152102935/226981)
(3162057889725670, -373846798334962768242035)
(1734754669135751433670/279841, 6547169695248859611635860557085/148035889)
(40899451690961944963365426660274574969463936130/5846632601568393018398400249889, 1774288780221692469547769062150837491790671200288090701655709557069495/14137047131184109719826020871227618913954768463)
(-1248003536758997154573948721713442602605/203889005748687573266436, 88857435136747111323960678419145694923133965825171987365965/92064184827845557595632584570957816)
(6630079061079052820680284864179834303680224130/1028994655418819466756573889809, 62094236808455048360283214302458245461422007380776897045718665932605/1043805734752943995337854883842773952389040377)
(8694946810095221692430035857703030/1428463328560791769, 75921576566851995298105566748886337268674277769095/1707275639234580941875141603)
(-954037104595888176774313976892131016849431030/77550797940028626775387698961, 114776620146949509411567215369857518989072731073459555786610942035/21596302703544227874728911102282401945981959)

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