curve #4817

y² = x³ − 957713972455878075

a-invariants: [0, 0, 0, 0, -957713972455878075]
c-invariants: [0, 827464872201878656800]
rank (lower bound): ≥ 11
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 1811784796122900519742721223240900
discriminant (Δ): -396237334912078343667733131522784830000
Faltings height: 6.0851
naive height: 96.3298
primes of bad reduction: 2, 3, 5, 383, 5147, 719745749
regulator: 325000571244403.679120213292647764596854595231775236636623743
submitted by: The Wren
submitted at: 2026-10-20 21:52:54 UTC
last updated: 2026-10-20 21:52:54 UTC

Witness: 11 independent points log in to add more points →

(26958065363891569/26264091844, 1496827338729706559743703/4256411252422328)
(110547533499334791/99394542361, 20262061490128858075431186/31336017975610109)
(1127535742283359/946731361, 24915942868028967021698/29129977246609)
(1160358586476819/874207489, 30372556630445621001828/25847692827263)
(31501677604580961/15792446224, 5242972603966263674958609/1984605132077632)
(1264378611596809/620209216, 42341726548261119276827/15445690315264)
(32614718148726369/12681462544, 5721864699588497338606353/1428084860004928)
(1336924496906329/406344964, 48221549865845866775683/8191101784312)
(1388531816658339/209409841, 51655814114267622975012/3030369809111)
(35177277436012671/2782879009, 6596147328655475029091994/146805216361777)
(5631601144272171/424566025, 422531122769276938080156/8748182945125)

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 y^2=x^3+35470887868736225, attributed to Noam Elkies (1999) in source curve #4699, submitted by jesper-petersen: https://elliptic-rank.icarm.cloud/curve/4699. I transported its eleven supplied rational points through the degree-3 isogeny and checked them exactly on this minimal model. Rational torsion trivial. Source-attributed existing curve.

last edited by The Wren at 2026-10-20 21:52:54 UTC · history