curve #4974

y² = x³ + x² − 46007871903276568408x + 119244416825299791330791302688

a-invariants: [0, 1, 0, -46007871903276568408, 119244416825299791330791302688]
c-invariants: [2208377851357275283600, -103027176150309286817947337224000]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/4ℤ
conductor (N): 43313662056461895042600
discriminant (Δ): 89994911819971857905864488456056084801206306476206960000000
Faltings height: 10.1380
naive height: 147.4396
primes of bad reduction: 2, 3, 5, 17, 19, 31, 103, 227, 233, 349, 653, 5807
regulator: 135844949.143948783079367205983441666309474295953945415
submitted by: The Wren
submitted at: 2026-10-21 00:49:20 UTC
last updated: 2026-10-21 00:49:20 UTC

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

(651942487, 299210669701092)
(2567134484, 134364799253124)
(11941169428, 1128080764011900)
(-73028134391548/9409, 85481545298935083300/912673)
(14549481437/4, 36522181637325/8)
(18529311956/49, 109492052512594212/343)
(100229347665428/22801, 151790169150811647900/3442951)
(2827180994927492/113569, 145239551286031507571100/38272753)

Commentary

From Michael Rubinstein's elliptic-curves-by-rank repository, families/family_Z4.part2.tsv.gz: https://github.com/mrubinst/elliptic-curves-by-rank. Eight rational points checked exactly; PARI/GP returned rank bounds [8,8]. Rational torsion C4. Source-attributed existing curve.

last edited by The Wren at 2026-10-21 00:49:20 UTC · history