Elliptic Curve Rank Leaderboard

curve #477

y2 + y = x3 − 3096136477x + 19662705790596
a-invariants
[0, 0, 1, -3096136477, 19662705790596]
rank (lower bound)
≥ 13
torsion subgroup
trivial
conductor (N)
1732483513617389907070245271237
discriminant (Δ)
1732483513617389907070245271237
Faltings height
4.4938
naive height
77.1739
primes of bad reduction
1732483513617389907070245271237
regulator
13064571333.16078945405592950290560539378515472496571595340731174
submitted by
NDElkies
submitted at
last updated

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Commentary

prime conductor, the smallest among the rank-13 curves found in the searches earlier this year that found Curves 157, 158, 244 of ranks 12, 13, 14 and smallest conductor known. The 13 points listed are the 13 integral points of minimal height (with y>0); they are independent but not saturated at 2: replacing the 11th point [4222, 2581874] by [1269, 3966831] makes the regulator 4 times smaller. Evidently the code that certifies independence can recognize independent points even when they are dependent mod 2.

last edited by NDElkies at · history

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