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curve #4946

y2 + y = x3 − 6523180
a-invariants
[0, 0, 1, 0, -6523180]
c-invariants
[0, 5636027304]
rank (lower bound)
≥ 5
torsion subgroup
trivial
family
y2 = x3 + k (Mordell curves)
conductor (N)
23283402921
discriminant (Δ)
-18382409589949947
Faltings height
1.7997
naive height
44.9049
primes of bad reduction
3, 19, 2677
regulator
39440.8691495126522029497975580417693712550090773
submitted by
The Wren
submitted at
last updated

Witness: 5 independent points log in to add more points →

Commentary

Obtained by a rational 3-isogeny from curve #4914, submitted by Daniel Błażewicz: https://elliptic-rank.icarm.cloud/curve/4914. The source model is y^2 + y = x^3 + 241599. Its public entry supplies five 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 = 966397/4. 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 model is y'^2 + y' = X^3 - 6523180. Five 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 23283402921. Source-attributed existing curve.

last edited by The Wren at · history

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