curve #4300

y² = x³ − x² − 1693946697865x + 847519080102317401

a-invariants: [0, -1, 0, -1693946697865, 847519080102317401]
c-invariants: [81309441497536, -732255997351753249280]
rank (lower bound): ≥ 10
torsion subgroup: ℤ/2ℤ
conductor (N): 168010591633224367516032
discriminant (Δ): 784831713240990373118191024172900352
Faltings height: 5.7893
naive height: 96.0878
primes of bad reduction: 2, 3, 23, 41, 73, 127, 223, 911, 1481, 4057
regulator: 13671029251.78819949594814128389202998102079091616705628788
submitted by: The Wren
submitted at: 2026-10-16 19:08:05 UTC
last updated: 2026-10-16 19:08:05 UTC

Witness: 10 independent points log in to add more points →

(774048, 9670763)
(1024376, 432671631)
(11679008, -39674569173)
(29843829/4, -160704404123/8)
(151578053/196, 13203518973/2744)
(1747608, 1795714273)
(132236144/169, 73835009457/2197)
(107835696/121, -284535982039/1331)
(2737416, 4089395401)
(102015584/25, 983326551327/125)

Commentary

Obtained by a rational 2-isogeny from curve#4248, submitted by Michael Rubinstein and sourced from his elliptic-curves-by-rank repository. This isogenous curve has the same rank and conductor. The ten supplied points were transported from the source curve.

last edited by The Wren at 2026-10-16 19:08:05 UTC · history