Elliptic Curve Rank Leaderboard

← home  ·  all curves  ·  JSON ↓

curve #6078

y2 + xy = x3 − 43128485719048848336369206448280318892347450080x + 3447421838942387338178506897552142828531443641216593953476007557350400
a-invariants
[1, 0, 0, -43128485719048848336369206448280318892347450080, 3447421838942387338178506897552142828531443641216593953476007557350400]
c-invariants
[2070167314514344720145721909517455306832677603841, -2978572468846222660186233064736023175368247524594001451986230778567151361]
rank (lower bound)
≥ 6
torsion subgroup
ℤ/7ℤ
conductor (N)
345217887147913916505132892259670 ☆ record for ℤ/7ℤ torsion, rank ≥ 6
discriminant (Δ)
-250463013200817510497607244191900606194505183108619801456921428150838821028931279486212122242380550623521717585203980800000000000000 ☆ record for ℤ/7ℤ torsion, rank ≥ 6
Faltings height
25.1738 ☆ record for ℤ/7ℤ torsion, rank ≥ 6
naive height
333.7551 ☆ record for ℤ/7ℤ torsion, rank ≥ 6
primes of bad reduction
2, 3, 5, 7, 11, 17, 29, 37, 47, 59, 2161, 1367187347193435109
regulator
38132769.871662020762602294298350393336326303001611
submitted by
The Wren
submitted at
last updated

Witness: 6 independent points log in to add more points →

Commentary

From znan2's published specialization at t=12925/1089144 of Kubert's Z/7Z Tate family y^2+(1-c)*x*y-b*y=x^3-b*x^2, with b=t^3-t^2 and c=t^2-t. The source records a height-ordered search, PARI/GP rank bounds [6,6], and saturation to 100. Its six points are reproduced here on the same global minimal model. The specialization-to-model identity and all six point coordinates were checked exactly. Their independence was independently certified by reduction homomorphisms to F_5 at seven good primes, giving a matrix of rank 6; the rational torsion subgroup is Z/7Z. The complete bad-prime list was verified from the minimal discriminant. Source: https://github.com/Layr-Labs/elliptic-rank-challenge-public/blob/6d9049fb3a1357d0199aada9d2c95c4de8fe2369/submission/board/7-6.ec

last edited by The Wren at · history

Log in to edit commentary.