curve #35

y² = x³ + x² − 1692310759026568999140789578145x + 839379398840982294584587970773038145228669599

a-invariants: [0, 1, 0, -1692310759026568999140789578145, 839379398840982294584587970773038145228669599]
c-invariants: [81230916433275311958757899750976, -725223800598609189906582606399776710024969039360]
rank (lower bound): ≥ 14
torsion subgroup: ℤ/2ℤ
conductor (N): 6116310391204554948397210171493960789901744808779000924864
discriminant (Δ): 5815704199930544426733052300699384236781490371077607532987271868542017804622894749291937792
Faltings height: 16.2313
naive height: 220.4245
primes of bad reduction: 2, 3, 7, 23, 43, 61, 79, 103, 157, 167, 179, 191, 199, 227, 229, 257, 271, 307, 487, 619, 1283, 3739
regulator: 1234880237432417.61331645290052732159258498172313923210000459986011
submitted by: David Renshaw
submitted at: 2026-05-27 22:12:13 UTC
last updated: 2026-07-01 22:44:39 UTC

(988927329611391, 11530632350958995292984)
(681925764652050, 1568465432141985518043)
(982479697930607, 11183605599461162465976)
(665315262684159, 2820867968019861832248)
(816133831449855, 1353961721252033023032)
(20572279820626749/25, 250389733064763724244532/125)
(681455320541454489/841, 8773166366975333247857352/24389)
(8076800853180114, 716978870073714829212603)
(7335280971697741/9, 33055815750694859233124/27)
(457957201387226901/529, 58522059114298646792700636/12167)
(127856380845197460021/625, 1445688913020859355673024573444/15625)
(435462740765918268153/157609, 8219252385969460300109469047112/62570773)
(811768719821415721233/18769, 23118208949065563006261517438272/2571353)
(299475331388281185601/345744, 983394088087157723809198920329/203297472)

Found by Fermigier (1996). A curve of rank exactly 14, via Dujella's elliptic-curve rank-records tables.

last edited by David Renshaw at 2026-05-27 22:32:07 UTC · history