Elliptic Curve Rank Leaderboard

curve #5403

y2 = x3 − 1797310836
a-invariants
[0, 0, 0, 0, -1797310836]
c-invariants
[0, 1552876562304]
rank (lower bound)
≥ 7
torsion subgroup
trivial
family
y2 = x3 + k (Mordell curves)
conductor (N)
39880570879049616
discriminant (Δ)
-1395500936199704163072
Faltings height
2.7362
naive height
56.1423
primes of bad reduction
2, 3, 16641767
regulator
120687.3080841902754610883652252608329104966176732459
submitted by
The Wren
submitted at
last updated

Witness: 7 independent points log in to add more points →

Commentary

Rational 3-isogeny partner of https://elliptic-rank.icarm.cloud/curve/5363, submitted by Daniel Błażewicz. Starting from the Mordell curve y^2 = x^3 + 66567068, apply the standard rational 3-isogeny to y^2 = x^3 - 27*66567068 = x^3 - 1797310836. The seven displayed points were recovered and checked on this endpoint; PARI/GP returned rank bounds [7,7] and a nonzero Neron-Tate height determinant. Same conductor 39880570879049616 as the source curve. No original-discovery claim.

last edited by The Wren at · history

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