curve #419

y² + xy = x³ − 24403746364851709763421313327110x + 46771399861468337270143023679331346542490944100

a-invariants: [1, 0, 0, -24403746364851709763421313327110, 46771399861468337270143023679331346542490944100]
rank (lower bound): ≥ 20
torsion subgroup: trivial
conductor (N): 658989802162463344814467347490126435199577916572310102653193642021710
discriminant (Δ): -14885095615487370251227862371409868728570596128315061788060679120737629177954766051012864000000
Faltings height: 16.8921
naive height: 228.4463
primes of bad reduction: 2, 3, 5, 11, 13, 23, 67, 71, 97, 25033, 5474941513, 35766196576289, 107450831973817, 27479811854284261
regulator: 4974204310558869387.13849793902319168332418682589926989236978960105849897551275
submitted by: Bhavik Mehta
submitted at: 2026-08-29 17:01:32 UTC
last updated: 2026-08-29 17:01:32 UTC

Witness: 20 independent points log in to add more points →

(8451110012225430, -666424481418004485647460)
(3332997885173220, 49594568540639629014090)
(-3779215305738180, 291585133086783195024090)
(30635822525765292, 5296461515418242101117482)
(-1751338986225180, 290067141257337131547090)
(343805644108190, 196015031774442561037940)
(-5705588120371590, 16459558222888631250840)
(2634222025455570, -27671491801216976312160)
(2403291740249820, -44755303846597934627910)
(-3547323656892180, -297828172238754284333910)
(187804517750100, 205413947850954984784290)
(2896939806311100, 19674559593995835379290)
(590332266258570, -180473840908719124223160)
(2490750751161420, -37946907306450405953910)
(-17665672493989740/49, -80821946938556976734126490/343)
(2322743181349140, -51178898042451438008310)
(2682580410857820, -24715868554360317683910)
(2838408784988040, -19272132846906695639730)
(3093014365655940, 29670175932522236031690)
(-4775955804492180, 233204285543296849146090)

Commentary

From Elkies's rank-17 K3 fibration (arXiv:2608.25406), specialized at t = 11. The 3 points beyond the seventeen generic sections came from searching the 1311 norm-4 quartic covers.

last edited by Bhavik Mehta at 2026-08-29 17:01:32 UTC · history