curve #4816

y² = x³ + 1245010169080772748

a-invariants: [0, 0, 0, 0, 1245010169080772748]
c-invariants: [0, -1075688786085787654272]
rank (lower bound): ≥ 11
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 57409271152390160973432335585906352
discriminant (Δ): -669621738721478837594114762274011689728
Faltings height: 6.1289
naive height: 96.8545
primes of bad reduction: 2, 3, 223, 14009, 3690091583
regulator: 8688108054764613.85067000874114034643803187048424846655234024
submitted by: The Wren
submitted at: 2026-10-20 21:51:00 UTC
last updated: 2026-10-20 21:51:00 UTC

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

(-33818108706294842/33555278761, 2891737489207732627511870/6146689518718741)
(-24896406637047602/48277317841, 11164984289199108410268770/10607540553342361)
(-23854386948275162/49845474121, 11858074231216920377123710/11128550397728581)
(6304243093926982/88230979369, 29247026146882780549116610/26207865418829653)
(2161857425219423926/1068173925625, 3408975206360919420503399326/1103984456481578125)
(10774111423677092926/3081797805025, 35876389877799338019671115326/5410111455710412625)
(12133885658871090238/3334863997921, 42809594227309455579727677890/6089998573307411281)
(13522138010853839638/3583679949721, 50297113227704648317534592990/6784124749298785981)
(40903805731410188782/7484256933169, 262600395334668506140478154530/20474958609576960553)
(167536014542048825926/19148369533225, 2170528730582897188481103610174/83791063014896279125)
(2434928540015113616557/181000348527769, 120182255078727350440944816855985/2435112985966088545853)

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^3-46111487743732324, attributed to Jordi Quer (1987) in source curve #4700, submitted by jesper-petersen: https://elliptic-rank.icarm.cloud/curve/4700. 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 21:51:01 UTC · history