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curve #4969

y2 + y = x3 − 12648616
a-invariants
[0, 0, 1, 0, -12648616]
c-invariants
[0, 10928404008]
rank (lower bound)
≥ 6
torsion subgroup
trivial
family
y2 = x3 + k (Mordell curves)
conductor (N)
94807395787347
discriminant (Δ)
-69114591528975963
Faltings height
1.9101
naive height
46.2293
primes of bad reduction
3, 223, 2801
regulator
6655778.1237937823575477389847674414566586578739894
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 #4968, submitted by Daniel Błażewicz: https://elliptic-rank.icarm.cloud/curve/4968. The source model is y^2 + y = x^3 + 468467. 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 = 1873869/4. Applied the degree-3 isogeny X = (x^3 + 4B)/x^2, V = Y*(x^3 - 8B)/x^3, then set y' = V - 1/2. The resulting minimal model is y'^2 + y' = X^3 - 12648616. 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 94807395787347. Source-attributed existing curve.

last edited by The Wren at · history

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