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Hilbert
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Q
\Q
Q
Elliptic curves over
Q
(
α
)
\Q(\alpha)
Q
(
α
)
Genus 2 curves over
Q
\Q
Q
Higher genus families
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F
q
\F_{q}
F
q
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p
p
p
-adic fields
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Weight
Degree
Include irrational
S
T
0
\mathrm{ST}^0
S
T
0
Maximal
no
yes
SO(1)
SO(2)
SO(3)
SO(4)
SO(5)
SO(6)
U(1)
SU(2)
U(1)_2
SU(2)_2
U(1)xU(1)
U(1)xSU(2)
SU(2)xSU(2)
USp(4)
U(1)_3
SU(2)_3
U(1)xU(1)_2
SU(2)xU(1)_2
U(1)xSU(2)_2
SU(2)xSU(2)_2
U(1)^3
U(1)^2xSU(2)
U(1)xSU(2)^2
SU(2)^3
U(1)xUSp(4)
SU(2)xUSp(4)
U(3)
USp(6)
yes
no
Components
Component group
P
r
[
a
1
=
0
]
\mathrm{Pr}[a_1=0]
P
r
[
a
1
=
0
]
Second trace moment
Fourth trace moment
First
a
2
a_2
a
2
moment
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degree
real dimension
component group
trace zero density
character diagonal
columns to display
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✓ components
✓ Pr[t=0]
✓ E[a_1^2]
✓ E[a_1^4]
E[a_1^6]
E[a_1^8]
E[a_1^{10}]
E[a_1^{12}]
✓ E[a_2]
E[a_2^2]
E[a_2^3]
E[a_2^4]
E[a_2^5]
E[a_2^6]
E[a_3^2]
E[a_3^4]
E[a_3^6]
maximal
rational
diagonal
show all
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CSV
Label
Wt
Deg
d
i
m
R
\mathrm{dim}_{\mathbb{R}}
d
i
m
R
G
0
\mathrm{G}^0
G
0
Name
G
/
G
0
\mathrm{G}/\mathrm{G}^0
G
/
G
0
P
r
[
t
=
0
]
\mathrm{Pr}[t\!=\!0]
P
r
[
t
=
0
]
E
[
a
1
2
]
\mathrm{E}[a_1^2]
E
[
a
1
2
]
E
[
a
1
4
]
\mathrm{E}[a_1^4]
E
[
a
1
4
]
E
[
a
1
6
]
\mathrm{E}[a_1^6]
E
[
a
1
6
]
E
[
a
1
8
]
\mathrm{E}[a_1^8]
E
[
a
1
8
]
E
[
a
1
10
]
\mathrm{E}[a_1^{10}]
E
[
a
1
1
0
]
E
[
a
1
12
]
\mathrm{E}[a_1^{12}]
E
[
a
1
1
2
]
E
[
a
2
]
\mathrm{E}[a_2]
E
[
a
2
]
E
[
a
2
2
]
\mathrm{E}[a_2^2]
E
[
a
2
2
]
E
[
a
2
3
]
\mathrm{E}[a_2^3]
E
[
a
2
3
]
E
[
a
2
4
]
\mathrm{E}[a_2^4]
E
[
a
2
4
]
E
[
a
2
5
]
\mathrm{E}[a_2^5]
E
[
a
2
5
]
E
[
a
2
6
]
\mathrm{E}[a_2^6]
E
[
a
2
6
]
E
[
a
3
2
]
\mathrm{E}[a_3^2]
E
[
a
3
2
]
E
[
a
3
4
]
\mathrm{E}[a_3^4]
E
[
a
3
4
]
E
[
a
3
6
]
\mathrm{E}[a_3^6]
E
[
a
3
6
]
Maximal
Rational
Diagonal
1.6.N.32.34a
1
1
1
6
6
6
1
1
1
U
(
1
)
3
\mathrm{U}(1)_{3}
U
(
1
)
3
J
(
A
(
4
,
4
)
)
J(A(4,4))
J
(
A
(
4
,
4
)
)
32
32
3
2
1
/
2
1/2
1
/
2
3
3
3
45
45
4
5
930
930
9
3
0
22575
22575
2
2
5
7
5
612738
612738
6
1
2
7
3
8
612738
612738
6
1
2
7
3
8
3
3
3
15
15
1
5
105
105
1
0
5
966
966
9
6
6
10398
10398
1
0
3
9
8
122802
122802
1
2
2
8
0
2
16
16
1
6
2478
2478
2
4
7
8
599200
599200
5
9
9
2
0
0
✓
[
1
,
3
,
10
,
7
,
18
,
76
,
79
,
123
,
177
,
83
,
46
,
384
,
444
,
1039
,
2052
,
1047
,
1101
,
2596
,
2295
,
689
]
[1, 3, 10, 7, 18, 76, 79, 123, 177, 83, 46, 384, 444, 1039, 2052, 1047, 1101, 2596, 2295, 689]
[
1
,
3
,
1
0
,
7
,
1
8
,
7
6
,
7
9
,
1
2
3
,
1
7
7
,
8
3
,
4
6
,
3
8
4
,
4
4
4
,
1
0
3
9
,
2
0
5
2
,
1
0
4
7
,
1
1
0
1
,
2
5
9
6
,
2
2
9
5
,
6
8
9
]
Download
displayed columns
for
results
to
Text
Pari/GP
SageMath
Magma
Oscar
CSV