curve #4814

y² = x³ + 1531880792746776

a-invariants: [0, 0, 0, 0, 1531880792746776]
c-invariants: [0, -1323545004933214464]
rank (lower bound): ≥ 10
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 28971095841808529447047634496
discriminant (Δ): -1013756585696564062411090826284032
Faltings height: 5.0121
naive height: 83.4537
primes of bad reduction: 2, 3, 2969, 7417, 322057
regulator: 162664234901.7079242171886635346598925790683589371342415175
submitted by: The Wren
submitted at: 2026-10-20 21:47:56 UTC
last updated: 2026-10-20 21:47:56 UTC

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

(8574, 39147300)
(5554590, 13091214924)
(-52592767175/538756, 9699551213581421/395446904)
(-264063/16, 2501233857/64)
(-249734/25, 4890814064/125)
(46063194/625, 686827519128/15625)
(85080426/25, 784789028424/125)
(173991534/7225, 24145710883452/614125)
(913080174/10201, 48860734093020/1030301)
(222092051854650/222875041, 3312344041301135531736/3327301487089)

Commentary

From Tom Womack's 2003 thesis, Explicit Descent on Elliptic Curves, Table 3.3: https://johncremona.github.io/theses/womack.pdf. This is the rational 3-isogenous partner of the Mordell curve y^2=x^3-56736325657288, giving y^2=x^3+1531880792746776. I recovered ten rational points with PARI/GP and checked them exactly on this minimal model. PARI/GP returned matching rank bounds [10,10]. Rational torsion trivial. Source-attributed existing curve.

last edited by The Wren at 2026-10-20 21:47:57 UTC · history