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Elliptic curves over $\Q$ of conductor 1006
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prime
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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
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order 12
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columns to display
✓ LMFDB curve label
Cremona curve label
✓ LMFDB class label
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class size
class degree
✓ conductor
discriminant
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Qbar-end algebra
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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
Adelic level
Adelic index
Adelic genus
Regulator
$Ш_{\textrm{an}}$
Ш primes
Integral points
Modular degree
Faltings height
j-invariant
Weierstrass coefficients
Weierstrass equation
mod-$m$ images
MW-generators
1006.a1
1006b2
1006.a
1006b
$2$
$2$
\( 2 \cdot 503 \)
\( 2^{3} \cdot 503^{2} \)
$0$
$\Z/2\Z$
$\Q$
$\mathrm{SU}(2)$
✓
$2$
8.6.0.6
2B
$4024$
$12$
$0$
$1$
$1$
$0$
$126$
$-0.099277$
$3687953625/2024072$
$[1, -1, 0, -32, 24]$
\(y^2+xy=x^3-x^2-32x+24\)
2.3.0.a.1
,
8.6.0.b.1
, 2012.6.0.?, 4024.12.0.?
$[]$
1006.a2
1006b1
1006.a
1006b
$2$
$2$
\( 2 \cdot 503 \)
\( - 2^{6} \cdot 503 \)
$0$
$\Z/2\Z$
$\Q$
$\mathrm{SU}(2)$
✓
$2$
8.6.0.1
2B
$4024$
$12$
$0$
$1$
$1$
$1$
$63$
$-0.445851$
$52734375/32192$
$[1, -1, 0, 8, 0]$
\(y^2+xy=x^3-x^2+8x\)
2.3.0.a.1
,
8.6.0.c.1
, 1006.6.0.?, 4024.12.0.?
$[]$
1006.b1
1006a1
1006.b
1006a
$1$
$1$
\( 2 \cdot 503 \)
\( - 2^{4} \cdot 503 \)
$1$
$\mathsf{trivial}$
$\Q$
$\mathrm{SU}(2)$
✓
$1006$
$2$
$0$
$0.284628487$
$1$
$6$
$48$
$-0.569676$
$-389017/8048$
$[1, 0, 1, -2, 4]$
\(y^2+xy+y=x^3-2x+4\)
1006.2.0.?
$[(1, 1)]$
1006.c1
1006e1
1006.c
1006e
$1$
$1$
\( 2 \cdot 503 \)
\( - 2^{12} \cdot 503 \)
$1$
$\mathsf{trivial}$
$\Q$
$\mathrm{SU}(2)$
✓
$1006$
$2$
$0$
$0.071754489$
$1$
$12$
$480$
$0.041440$
$-270212594625/2060288$
$[1, -1, 1, -135, 639]$
\(y^2+xy+y=x^3-x^2-135x+639\)
1006.2.0.?
$[(3, 14)]$
1006.d1
1006d1
1006.d
1006d
$1$
$1$
\( 2 \cdot 503 \)
\( - 2^{10} \cdot 503 \)
$1$
$\mathsf{trivial}$
$\Q$
$\mathrm{SU}(2)$
✓
$1006$
$2$
$0$
$0.106360665$
$1$
$8$
$120$
$-0.194395$
$-1349232625/515072$
$[1, 1, 1, -23, 45]$
\(y^2+xy+y=x^3+x^2-23x+45\)
1006.2.0.?
$[(3, 2)]$
1006.e1
1006c1
1006.e
1006c
$1$
$1$
\( 2 \cdot 503 \)
\( - 2^{4} \cdot 503 \)
$1$
$\mathsf{trivial}$
$\Q$
$\mathrm{SU}(2)$
✓
$1006$
$2$
$0$
$0.324915587$
$1$
$4$
$96$
$-0.561197$
$13651919/8048$
$[1, 0, 0, 5, 1]$
\(y^2+xy=x^3+5x+1\)
1006.2.0.?
$[(0, 1)]$
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