Elliptic Curve Rank Leaderboard

curve #71

y2 = x3 − x2 − 75x − 134
a-invariants
[0, -1, 0, -75, -134]
c-invariants
[3616, 137440]
rank (lower bound)
≥ 4
torsion subgroup
trivial
conductor (N)
16430032
discriminant (Δ)
16430032
Faltings height
0.0861
naive height
24.5794
primes of bad reduction
2, 353, 2909
regulator
29.93011794279284801770139339930493926616246710
submitted by
David Renshaw
submitted at
last updated

Witness: 4 independent points log in to add more points →

Commentary

Provenance: found by a local bounded-height search over reduced integral Weierstrass models. Invariants are c4=3616, c6=137440, Delta=16430032 = 2^4*353*2909. The submitted points (-2,2), (-6,8), (10,4), (30,154) were checked exactly on the curve, with an additional finite-field independence sanity check; the site Neron-Tate verifier gives the definitive certificate.

last edited by David Renshaw at · history

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