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curve #4944

y2 + y = x3 − 5899291
a-invariants
[0, 0, 1, 0, -5899291]
c-invariants
[0, 5096987208]
rank (lower bound)
≥ 6
torsion subgroup
trivial
family
y2 = x3 + k (Mordell curves)
conductor (N)
20623188949947
discriminant (Δ)
-15034304744511363
Faltings height
1.7830
naive height
44.7038
primes of bad reduction
3, 317, 919
regulator
4631310.1299671670330872465028383728990916640537402
submitted by
The Wren
submitted at
last updated

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

Commentary

Obtained by a rational 3-isogeny from curve #4908, submitted by Daniel Błażewicz: https://elliptic-rank.icarm.cloud/curve/4908. The source model is y^2 + y = x^3 + 218492. Its public entry supplies six rational points and no commentary identifying an earlier source. Completed the square with Y = y + 1/2, giving Y^2 = x^3 + B with B = 873969/4. Applied the standard degree-3 isogeny X = (x^3+4*B)/x^2, V = Y*(x^3-8*B)/x^3, then set y' = V - 1/2. The resulting integral model is y'^2 + y' = X^3 - 5899291. Six supplied rational points transported through this map and checked exactly on the target curve. Rational torsion trivial. Same rank and conductor as the source; conductor 20623188949947. Source-attributed existing curve.

last edited by The Wren at · history

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