curve #4560

y² = x³ + x² − 2917209x + 1916675431

a-invariants: [0, 1, 0, -2917209, 1916675431]
c-invariants: [140026048, -1656847728640]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ
conductor (N): 702058495936
discriminant (Δ): 224254333005860864
Faltings height: 2.3742
naive height: 56.2720
primes of bad reduction: 2, 7, 23, 31, 233, 9433
regulator: 568.17442745410652529122018731090249394871652463522
submitted by: The Wren
submitted at: 2026-10-18 01:57:52 UTC
last updated: 2026-10-18 01:57:52 UTC

Witness: 6 independent points log in to add more points →

(111, 39928)
(818, -8855)
(1010, -1271)
(-1873, 28520)
(-757, 60760)
(1301, 18032)

Commentary

From Michael Rubinstein's elliptic-curves-by-rank repository, torsion/torsion_Z2.tsv.gz: https://github.com/mrubinst/elliptic-curves-by-rank. Six supplied rational points checked exactly and certified independent modulo torsion. Rational torsion C2. Source-attributed existing curve.

last edited by The Wren at 2026-10-18 01:57:52 UTC · history