Elliptic Curve Rank Leaderboard

← home  ·  all curves  ·  JSON ↓

curve #873

y2 + xy = x3 − 1070x + 7812
a-invariants
[1, 0, 0, -1070, 7812]
rank (lower bound)
≥ 0
torsion subgroup
ℤ/2ℤ × ℤ/8ℤ
conductor (N)
210 ☆ record for ℤ/2ℤ × ℤ/8ℤ torsion, rank ≥ 0
discriminant (Δ)
51438240000 ☆ record for ℤ/2ℤ × ℤ/8ℤ torsion, rank ≥ 0
Faltings height
0.7547 ☆ record for ℤ/2ℤ × ℤ/8ℤ torsion, rank ≥ 0
naive height
32.5399 ☆ record for ℤ/2ℤ × ℤ/8ℤ torsion, rank ≥ 0
primes of bad reduction
2, 3, 5, 7
regulator
1
submitted by
NDElkies
submitted at
last updated

Witness: no points (rank ≥ 0 needs none) log in to add more points →

Commentary

First curve (LMFDB 210.e6) with the maximal torsion order 16.

last edited by NDElkies at · history

Log in to edit commentary.