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Elliptic curves over $\Q$ of conductor 19
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Conductor
prime
p-power
sq-free
divides
j-invariant
Rank
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Complex multiplication
trivial
order 4
order 8
order 12
ℤ/2ℤ
ℤ/3ℤ
ℤ/4ℤ
ℤ/5ℤ
ℤ/6ℤ
ℤ/7ℤ
ℤ/8ℤ
ℤ/9ℤ
ℤ/10ℤ
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ℤ/2ℤ⊕ℤ/2ℤ
ℤ/2ℤ⊕ℤ/4ℤ
ℤ/2ℤ⊕ℤ/6ℤ
ℤ/2ℤ⊕ℤ/8ℤ
no potential CM
potential CM
CM field Q(sqrt(-1))
CM field Q(sqrt(-3))
CM field Q(sqrt(-7))
CM discriminant -3
CM discriminant -4
CM discriminant -7
CM discriminant -8
CM discriminant -11
CM discriminant -12
CM discriminant -16
CM discriminant -19
CM discriminant -27
CM discriminant -28
CM discriminant -43
CM discriminant -67
CM discriminant -163
Bad$\ p$
include
exclude
exactly
subset
Discriminant
Regulator
Analytic order of Ш
Galois image
Isogeny class size
Isogeny class degree
Cyclic isogeny degree
$p\ $div$\ $|Ш|
include
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subset
Nonmax$\ \ell$
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▲ conductor
rank
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analytic Ш
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✓ LMFDB curve label
Cremona curve label
✓ LMFDB class label
Cremona class label
class size
class degree
✓ conductor
discriminant
✓ rank
✓ torsion
Qbar-end algebra
✓ CM discriminant
Sato-Tate group
semistable
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nonmaximal primes
ℓ-adic images
mod-ℓ images
regulator
analytic Ш
ш primes
integral points
modular degree
Faltings height
j-invariant
Weierstrass coeffs
✓ Weierstrass equation
Results (3 matches)
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Label
Cremona label
Class
Cremona class
Class size
Class degree
Conductor
Discriminant
Rank
Torsion
$\textrm{End}^0(E_{\overline\Q})$
CM
Sato-Tate
Semistable
Potentially good
Nonmax $\ell$
$\ell$-adic images
mod-$\ell$ images
Regulator
$Ш_{\textrm{an}}$
Ш primes
Integral points
Modular degree
Faltings height
j-invariant
Weierstrass coefficients
Weierstrass equation
19.a1
19a2
19.a
19a
$3$
$9$
\( 19 \)
\( -19 \)
$0$
$\mathsf{trivial}$
$\Q$
$\mathrm{SU}(2)$
✓
$3$
27.72.0.2
3B.1.2
$1$
$1$
$0$
$3$
$0.033439$
$-50357871050752/19$
$[0, 1, 1, -769, -8470]$
\(y^2+y=x^3+x^2-769x-8470\)
19.a2
19a1
19.a
19a
$3$
$9$
\( 19 \)
\( - 19^{3} \)
$0$
$\Z/3\Z$
$\Q$
$\mathrm{SU}(2)$
✓
$3$
9.72.0.3
3Cs.1.1
$1$
$1$
$2$
$1$
$-0.515867$
$-89915392/6859$
$[0, 1, 1, -9, -15]$
\(y^2+y=x^3+x^2-9x-15\)
19.a3
19a3
19.a
19a
$3$
$9$
\( 19 \)
\( -19 \)
$0$
$\Z/3\Z$
$\Q$
$\mathrm{SU}(2)$
✓
$3$
27.72.0.1
3B.1.1
$1$
$1$
$2$
$3$
$-1.065172$
$32768/19$
$[0, 1, 1, 1, 0]$
\(y^2+y=x^3+x^2+x\)
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