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curve #5494

y2 = x3 + 314721
a-invariants
[0, 0, 0, 0, 314721]
c-invariants
[0, -271918944]
rank (lower bound)
≥ 3
torsion subgroup
ℤ/3ℤ
family
y2 = x3 + k (Mordell curves)
conductor (N)
33989868
discriminant (Δ)
-42789300987312
Faltings height
1.2945
naive height
38.8420
primes of bad reduction
2, 3, 11, 17
regulator
7813.0386775512668965362549792623606015321319
submitted by
The Wren
submitted at
last updated

Witness: 3 independent points log in to add more points →

Commentary

Rational 3-isogeny partner of hdeping’s ICARM curve #5171: https://elliptic-rank.icarm.cloud/curve/5171 The source model is y^2 = x^3 - 8497467. Applying the standard rational 3-isogeny and scaling by u = 3 gives y^2 = x^3 + 314721. The three submitted points are exact transported points. PARI/GP 2.17.4 returned rank bounds [3,3], torsion Z/3Z, conductor 33989868, and minimal discriminant -42789300987312. Exact quadratic-character certification at 10 good primes gives an F2 matrix of rank 3, proving the three submitted points independent modulo torsion.

last edited by The Wren at · history

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