curve #310

y² + xy = x³ − 1873940813132840352272936419410635778826863x + 987165421651192729341038595063275202627467898519141617381276217

a-invariants

[1, 0, 0, -1873940813132840352272936419410635778826863, 987165421651192729341038595063275202627467898519141617381276217]

c-invariants

[89949159030376336909100948131710517383689425, -852910924306630518150792269873215339575495915742735923193498185625]

rank (lower bound)

≥ 18

torsion subgroup

ℤ/2ℤ

conductor (N)

288223154151653778337307627146202434973670195623654112440970678577409850

discriminant (Δ)

178366552240819613635837756699513126037238421271340078083424114134861955668984171479187414542891604318460528025744022574000000

Faltings height

23.0216

naive height

303.6235

primes of bad reduction

2, 3, 5, 7, 11, 19, 29, 41, 43, 47, 73, 89, 131, 139, 239, 271, 353, 421, 541, 1093, 1213, 1559, 1597, 2137, 41863, 11763979, 120637667

regulator

9792851245076258851381.2083748279069287225028655192936596116369325970411194

submitted by

7fff-zip

submitted at

2026-08-24 00:23:41 UTC

later contributions

rank ≥ 15 → ≥ 18 · David Renshaw · 2026-09-02 19:07:07 UTC

Witness: 18 independent points log in to add more points →

(733164632783236931406, 2712297234378665520828327655389)
(803458953340555152702, 448155739340382090493741517349)
(808823303863052894442, 778905581281286150799320607729)
(-1879683142575841985650568618971218/1335593951041, 44652884982317714244731816538224592046117988336811/1543517881745111839)
(-809590187497628187006002/729, 811218393581578694725894973575450127/19683)
(4187343008092300585768/9, 396825315440980656314341847654273/27)
(27560511846382349461387/36, 239670967554762426888664342655689/216)
(1436375503507518426322368/5329, 8712999215327311928155957143171663693/389017)
(3216171233556992841329646/3721, 823848707955968661766341888211038489/226981)
(5145581485130858492645022/6241, 793971453090368039811079377584732331/493039)
(378072665489897958886698627/470596, 143142482990686696014945953677251756789/322828856)
(106327561137593900633940138/54289, 879085028321115462592342627253631358473/12649337)
(118536180425196164655458364/134689, 218853212973688680946685743121217891747/49430863)
(362302954823491522036901118/966289, 17443753065571635386324797533577236304803/949862087)
(4952909599841788070595013881269/6871083664, 1881417907916058379903000830470654131490010937/569557867076288)
(1416734254094179884827878825752/1759886401, 40721012822926457833461694655750308575903099/73828994408351)
(1631607022217452960364298299952/42915601, 2082790325147894889156228918015355095847661949/281140102151)
(526731437575859274739685732149572/689964470881, 699722409379246741955784466406668533166329379599/573112778057064721)

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