curve #1833

y² + xy = x³ − 37680956700999226080263982005713090640x − 36992898397926078743894505902555362159162611772488902400

a-invariants: [1, 0, 0, -37680956700999226080263982005713090640, -36992898397926078743894505902555362159162611772488902400]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 109044022306006841937603510 ☆ record for ℤ/2ℤ × ℤ/6ℤ torsion, rank ≥ 6
discriminant (Δ): 2832913457088057836879504753557297495186356712128361067181341227400250949632009768272301845986874081364934656000000 ☆ record for ℤ/2ℤ × ℤ/6ℤ torsion, rank ≥ 6
Faltings height: 20.6552 ☆ record for ℤ/2ℤ × ℤ/6ℤ torsion, rank ≥ 6
naive height: 271.1803 ☆ record for ℤ/2ℤ × ℤ/6ℤ torsion, rank ≥ 6
primes of bad reduction: 2, 3, 5, 7, 19, 31, 59, 79, 97, 179, 673, 92641, 174721
regulator: 22452561.318851913189450416475415226292215063752967
submitted by: dujella
submitted at: 2026-09-25 16:10:33 UTC
last updated: 2026-09-25 16:10:33 UTC

(-2989863404519469920, 6995768683639734630607549360)
(10655036526409965352, 27770115828849915693054478576)
(-1612366285436148320, 4423900631065189129485603760)
(540264925906143942595/4, 12544631527256833935404497716455/8)
(20269619893966105186720/169, 2882001444306457588145290707326320/2197)
(-77923188462673412909706080/23746129, 828968027924538661366491705732719337520/115714886617)

found Elkies (2006)

last edited by dujella at 2026-09-25 16:10:33 UTC · history