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curve #70

y2 + xy + y = x3 − x2 − 6x
a-invariants
[1, -1, 1, -6, 0]
c-invariants
[273, 999]
rank (lower bound)
≥ 3
torsion subgroup
trivial
conductor (N)
11197
discriminant (Δ)
11197
Faltings height
-0.5324
naive height
16.8284 ★ record for rank ≥ 3
primes of bad reduction
11197
regulator
0.86842195369372664900484860186367158964425101
submitted by
David Renshaw
submitted at
last updated

Witness: 3 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=273, c6=999, Delta=11197. The submitted points (0,0), (-1,2), (-2,1) 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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