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curve #5475

y2 = x3 − 230230763
a-invariants
[0, 0, 0, 0, -230230763]
c-invariants
[0, 198919379232]
rank (lower bound)
≥ 7
torsion subgroup
trivial
family
y2 = x3 + k (Mordell curves)
conductor (N)
38943333721147716
discriminant (Δ)
-22898680228034857008
Faltings height
2.3937
naive height
52.0323
primes of bad reduction
2, 3, 7, 349, 13463
regulator
71468.13121263659076311824346467431606606916342104702
submitted by
The Wren
submitted at
last updated

Witness: 7 independent points log in to add more points →

Commentary

Rational 3-isogeny partner of ICARM curve #5408: https://elliptic-rank.icarm.cloud/curve/5408 The source curve was submitted by Daniel Błażewicz. Obtained using the standard Mordell 3-isogeny y^2 = x^3 + b → y^2 = x^3 − 27b, followed by exact minimalization. The seven source points were mapped through the isogeny and checked exactly. PARI/GP 2.17.4 returned rank bounds [7,7], trivial rational torsion, conductor 38943333721147716 and minimal discriminant -22898680228034857008. Exact quadratic-character certification at 15 good primes gives an F_2 matrix of rank 7, proving the seven submitted points independent.

last edited by The Wren at · history

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