Elliptic Curve Rank Leaderboard

curve #3756

y2 = x3 + x2 − 298553x + 59896048
a-invariants
[0, 1, 0, -298553, 59896048]
rank (lower bound)
≥ 6
torsion subgroup
ℤ/2ℤ
conductor (N)
341505273100
discriminant (Δ)
148151817576242000
Faltings height
2.0533
naive height
49.4337
primes of bad reduction
2, 5, 29, 61, 89, 109, 199
regulator
601.52942782586698096119920737325833409621744709412
submitted by
jesper-petersen
submitted at
last updated

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

Commentary

Found 2026-10-01 in a discriminant-first search for elliptic curves over Q with rational 2-torsion. The search used the visible-2-torsion family y^2 = x^3 + A*x^2 + B*x and a Kretschmer-type four-square pattern with B = 5*109*199 = 108455 and A = 1105. PARI/GP 2.17.4 on the global minimal model gives ellrank bounds [6,6], torsion Z/2Z, conductor 341505273100, and minimal discriminant 148151817576242000. The six submitted points are the independent generators returned by ellrank(E,1).

last edited by jesper-petersen at · history

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