curve #4979

y² + xy + y = x³ − x² + 3153356070811679245x + 5524302940347287085239841122

a-invariants: [1, -1, 1, 3153356070811679245, 5524302940347287085239841122]
c-invariants: [-151361091398960603775, -4772997741141180952942545446625]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/4ℤ
conductor (N): 572253855656441153033475
discriminant (Δ): -15190519261744107850897132334205181105581096441764627109375
Faltings height: 9.8465
naive height: 141.2811
primes of bad reduction: 3, 5, 7, 13, 17, 29, 149, 179, 191, 607, 823, 22277
regulator: 1769749.50273314087128581817653133937780200629465726863
submitted by: The Wren
submitted at: 2026-10-21 00:58:28 UTC
last updated: 2026-10-21 00:58:28 UTC

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

(-4391165829/4, 217565638878725/8)
(-956353170, 40421875568356)
(-825764751, 48552385554175)
(328100734, 81204770872020)
(439902288, 83645453888590)
(54877268934, 12862408993787245)
(84527711709/16, 26359046393766625/64)
(30995483641/9, 6459219841891925/27)

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 00:58:28 UTC · history