curve #1976

y² + xy = x³ − x² − 47377997631934616131259094x + 122064326885475393485584567015835076600

a-invariants: [1, -1, 0, -47377997631934616131259094, 122064326885475393485584567015835076600]
rank (lower bound): ≥ 15
torsion subgroup: ℤ/2ℤ
conductor (N): 74982942042145889714439140878353729492075810 ☆ record for ℤ/2ℤ torsion, rank ≥ 15
discriminant (Δ): 369613849346134632045712208014198505337165268784681578572945276508115295907500
Faltings height: 13.6588
naive height: 188.9742
primes of bad reduction: 2, 3, 5, 7, 13, 41, 47, 61, 137, 167, 293, 1223, 1367, 1439, 2243, 2557, 3253, 90289
regulator: 2548596661806.1850299206938448046198400829964479978403371144171355773
submitted by: dujella
submitted at: 2026-09-25 20:18:59 UTC
last updated: 2026-09-25 20:18:59 UTC

(4500895301116, 17895577089353792)
(-7879047179700, -2496274582710240120)
(-7791526340259, -4266631333507969158)
(-7816770890871, -3845470103309695578)
(-7919982209319, -712375905043009743)
(-7861912714884, -2933213810436686208)
(-7921327767924, -563899328680245528)
(-7679614164996, -5743906466119247676)
(-7898698253999, -1869092036434260498)
(-7858400307321, -3014687899238193876)
(-7918000894850, -886766356327884100)
(-7916835300134, -974847693981397408)
(-7902140608214, -1735516496710803088)
(-7787026675214, -4337047328172214698)
(-7830443686839, -3595099957696460463)

found by Elkies (2009)

last edited by dujella at 2026-09-25 20:18:59 UTC · history