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curve #4943

y2 + y = x3 − 844
a-invariants
[0, 0, 1, 0, -844]
c-invariants
[0, 729000]
rank (lower bound)
≥ 1
torsion subgroup
trivial
family
y2 = x3 + k (Mordell curves)
conductor (N)
675
discriminant (Δ)
-307546875
Faltings height
0.3076
naive height
26.9989
primes of bad reduction
3, 5
regulator
1.216773260922917078654279593465475939824
submitted by
The Wren
submitted at
last updated

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Commentary

Obtained by a rational 3-isogeny from curve #4873, submitted by Daniel Błażewicz: https://elliptic-rank.icarm.cloud/curve/4873. The source model is y^2 + y = x^3 + 31. Its public entry supplies one rational point and no commentary identifying an earlier source. Completed the square with Y = y + 1/2, giving Y^2 = x^3 + B with B = 125/4. 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 - 844. One supplied rational point transported through this map and checked exactly on the target curve. Rational torsion trivial. Same rank and conductor as the source; conductor 675. Source-attributed existing curve.

last edited by The Wren at · history

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