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Elliptic curves over $\Q$ of conductor 39
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Conductor
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
trivial
order 4
order 8
order 12
ℤ/2ℤ
ℤ/3ℤ
ℤ/4ℤ
ℤ/5ℤ
ℤ/6ℤ
ℤ/7ℤ
ℤ/8ℤ
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ℤ/10ℤ
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ℤ/2ℤ⊕ℤ/2ℤ
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ℤ/2ℤ⊕ℤ/8ℤ
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Label
Cremona label
Class
Cremona class
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Rank
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$\textrm{End}^0(E_{\overline\Q})$
CM
Sato-Tate
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$\ell$-adic images
mod-$\ell$ images
Adelic level
Adelic index
Adelic genus
Regulator
$Ш_{\textrm{an}}$
Ш primes
Integral points
Modular degree
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j-invariant
$abc$ quality
Szpiro ratio
Weierstrass coefficients
Weierstrass equation
mod-$m$ images
MW-generators
39.a1
39a2
39.a
39a
$4$
$4$
\( 3 \cdot 13 \)
\( 3^{4} \cdot 13 \)
$0$
$\Z/2\Z$
$\Q$
$\mathrm{SU}(2)$
✓
$2$
4.12.0.8
2B
$312$
$48$
$0$
$1$
$1$
$0$
$4$
$-0.318367$
$37159393753/1053$
$1.11616$
$6.64339$
$[1, 1, 0, -69, -252]$
\(y^2+xy=x^3+x^2-69x-252\)
2.3.0.a.1
,
4.12.0-4.c.1.2
,
24.24.0-24.ba.1.16
,
26.6.0.b.1
,
52.24.0-52.g.1.1
, $\ldots$
$[]$
39.a2
39a3
39.a
39a
$4$
$4$
\( 3 \cdot 13 \)
\( 3 \cdot 13^{4} \)
$0$
$\Z/4\Z$
$\Q$
$\mathrm{SU}(2)$
✓
$2$
4.12.0.7
2B
$312$
$48$
$0$
$1$
$1$
$2$
$4$
$-0.318367$
$822656953/85683$
$0.96086$
$5.60330$
$[1, 1, 0, -19, 22]$
\(y^2+xy=x^3+x^2-19x+22\)
2.3.0.a.1
,
4.12.0-4.c.1.1
,
12.24.0-12.h.1.2
, 104.24.0.?, 312.48.0.?
$[]$
39.a3
39a1
39.a
39a
$4$
$4$
\( 3 \cdot 13 \)
\( 3^{2} \cdot 13^{2} \)
$0$
$\Z/2\Z\oplus\Z/2\Z$
$\Q$
$\mathrm{SU}(2)$
✓
$2$
4.12.0.1
2Cs
$156$
$48$
$0$
$1$
$1$
$2$
$2$
$-0.664940$
$10218313/1521$
$0.91403$
$4.40546$
$[1, 1, 0, -4, -5]$
\(y^2+xy=x^3+x^2-4x-5\)
2.6.0.a.1
,
4.12.0-2.a.1.1
,
12.24.0-12.a.1.1
,
52.24.0-52.b.1.2
, 156.48.0.?
$[]$
39.a4
39a4
39.a
39a
$4$
$4$
\( 3 \cdot 13 \)
\( - 3 \cdot 13 \)
$0$
$\Z/2\Z$
$\Q$
$\mathrm{SU}(2)$
✓
$2$
8.12.0.6
2B
$312$
$48$
$0$
$1$
$1$
$1$
$4$
$-1.011513$
$12167/39$
$0.85844$
$2.98048$
$[1, 1, 0, 1, 0]$
\(y^2+xy=x^3+x^2+x\)
2.3.0.a.1
,
4.6.0.c.1
,
8.12.0-4.c.1.5
,
12.12.0-4.c.1.2
,
24.24.0-24.ba.1.4
, $\ldots$
$[]$
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displayed columns
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