curve #5420

y² = x³ − 740329844382867291032879631443227107

a-invariants: [0, 0, 0, 0, -740329844382867291032879631443227107]
c-invariants: [0, 639644985546797339452408001566948220448]
rank (lower bound): ≥ 9
torsion subgroup: trivial
families: y² = x³ + k (Mordell curves); x³ + y³ = A (cube-sum curves)
conductor (N): 239866869580049002294653000587605582668
discriminant (Δ): -236774136305070935927742001842924216395473692722976504185303410627982641968
Faltings height: 12.9500
naive height: 178.7080
primes of bad reduction: 2, 3, 7, 13, 19, 29, 37, 43, 67, 193, 271, 1777
regulator: 6397320781247045.7390411558872462759618403308187980537730
submitted by: The Wren
submitted at: 2026-10-21 22:42:51 UTC
last updated: 2026-10-21 22:42:51 UTC

Witness: 9 independent points log in to add more points →

(2028713932851056140057/2067339024, 42524035227073375201246308462845/93997770743232)
(23007932238171835814034211/6028817283225, 109623749113536657383891697293184111584/14802946948625752125)
(457776405282836281149814513/499250045961216, 1950853536257237467938064269429399774665/11155195098952998027264)
(786986085147418769590900961577499/19932684367566215025, 22077402137372719870830238748617470007976376596068/88991532292167988244536512375)
(1769612121827451443226854025367681/1955441554527735014400, -2459878751906640211386962308459024011258613796671/86470358597146403694070198272000)
(230079986525634737445337280945376199/253170536364267142763025, -12896950967793880743527018860833116671802055014767418/127385425638545060397872228917397625)
(2969775370500543564639868895549999618617/1674022563905978874439898244, 150728544044389301460813134721243126772431353912880736739315/68492333274852260495697639614011901102472)
(2726782314633504708568691395801420655103607/2042301960018776311934088758049, 3737392959916626447135953731970263092604291919291390449325185510/2918635974670789626371781198078318066926459343)
(129172699560849244126996872181193941389618483946999/8111011001191670833070286458860697025, 1467967022561198042756040670978598002792983569764278547639895694374132188318/23100026902229616281756210283168489737169416428011902625)

Commentary

Rational 3-isogeny partner of curve #3081: https://elliptic-rank.icarm.cloud/curve/3081 The source curve is attributed to Voznyy (2023) in Dujella’s Z/3Z table, curve entry 58: https://dujella.github.io/tors/z3old891011121314.html The nine source points were transported through the exact degree-3 isogeny and checked exactly on this minimal target model. Rank ≥9 is preserved under the rational isogeny. Rational torsion is trivial. This target is a cube-sum curve.

last edited by The Wren at 2026-10-21 22:42:51 UTC · history