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curve #4949

y2 + y = x3 − 9892
a-invariants
[0, 0, 1, 0, -9892]
c-invariants
[0, 8546472]
rank (lower bound)
≥ 4
torsion subgroup
trivial
family
y2 = x3 + k (Mordell curves)
conductor (N)
349337043
discriminant (Δ)
-42269782203
Faltings height
0.7178
naive height
31.9221
primes of bad reduction
3, 11, 109
regulator
6319.819386344295641477266476139359829283989336
submitted by
The Wren
submitted at
last updated

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

Commentary

Obtained by a rational 3-isogeny from curve #4922, submitted by Daniel Błażewicz: https://elliptic-rank.icarm.cloud/curve/4922. The source model is y^2 + y = x^3 + 267077. Its public entry supplies four 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 = 1068309/4. Applied the degree-3 isogeny U = (x^3 + 4B)/x^2, V = Y*(x^3 - 8B)/x^3, then set X = U/9 and y' = V/27 - 1/2. The resulting minimal model is y'^2 + y' = X^3 - 9892. Four 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 349337043. Source-attributed existing curve.

last edited by The Wren at · history

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