curve #4671

y² = x³ + x² + 106812055x + 1112875415719

a-invariants: [0, 1, 0, 106812055, 1112875415719]
c-invariants: [-5126978624, -961493597309440]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/2ℤ
conductor (N): 148797332771970176
discriminant (Δ): -612984511215390704222199808
Faltings height: 3.8225
naive height: 68.9990
primes of bad reduction: 2, 7, 17, 41, 79, 103, 167, 271, 647
regulator: 34395130.0477348701786762358979015335736246533222152985
submitted by: The Wren
submitted at: 2026-10-20 20:17:22 UTC
last updated: 2026-10-20 20:17:22 UTC

Witness: 8 independent points log in to add more points →

(-45014/9, 18183599/27)
(178674, -75659033)
(69642, 18609691)
(72141/4, -23874221/8)
(136554, 50616587)
(30162, 5636951)
(906741/4, -864365521/8)
(-728646/121, 667272223/1331)

Commentary

I obtained this curve as a rational 2-isogenous partner of curve #4651: https://elliptic-rank.icarm.cloud/curve/4651. The source curve appears in Michael Rubinstein's elliptic-curves-by-rank repository, torsion/torsion_Z2.tsv.gz: https://github.com/mrubinst/elliptic-curves-by-rank. I transported eight supplied independent rational points through the isogeny and checked them exactly on this minimal model. Same rank and conductor; rational torsion Z/2Z. Source-attributed isogeny construction.

last edited by The Wren at 2026-10-20 20:17:22 UTC · history