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curve #1073

y2 + xy = x3 − 49423080x + 130545230400
a-invariants
[1, 0, 0, -49423080, 130545230400]
rank (lower bound)
≥ 1
torsion subgroup
ℤ/2ℤ × ℤ/8ℤ
conductor (N)
82110 ☆ record for ℤ/2ℤ × ℤ/8ℤ torsion, rank ≥ 1
discriminant (Δ)
363628103290905600000000 ☆ record for ℤ/2ℤ × ℤ/8ℤ torsion, rank ≥ 1
Faltings height
3.3010 ☆ record for ℤ/2ℤ × ℤ/8ℤ torsion, rank ≥ 1
naive height
64.7614 ☆ record for ℤ/2ℤ × ℤ/8ℤ torsion, rank ≥ 1
primes of bad reduction
2, 3, 5, 7, 17, 23
regulator
2.034865242181593696521637625278328301143
submitted by
David Renshaw
submitted at
last updated

Witness: 1 independent point log in to add more points →

Commentary

Cremona 82110bt2 = LMFDB 82110.bs5: https://www.lmfdb.org/EllipticCurve/Q/82110/bs/5 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 82110, minimal discriminant 363628103290905600000000, torsion ℤ/2ℤ × ℤ/8ℤ. The witness is the generator from Cremona's tables.

last edited by David Renshaw at · history

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