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Hilbert
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Elliptic curves over
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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✓ degree
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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
Results (unique match)
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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.96.67a
1
1
1
6
6
6
1
1
1
U
(
1
)
3
\mathrm{U}(1)_{3}
U
(
1
)
3
B
(
O
,
2
)
B(O,2)
B
(
O
,
2
)
96
96
9
6
1
/
12
1/12
1
/
1
2
4
4
4
42
42
4
2
660
660
6
6
0
12880
12880
1
2
8
8
0
292824
292824
2
9
2
8
2
4
292824
292824
2
9
2
8
2
4
2
2
2
11
11
1
1
75
75
7
5
622
622
6
2
2
5832
5832
5
8
3
2
60247
60247
6
0
2
4
7
16
16
1
6
1518
1518
1
5
1
8
268960
268960
2
6
8
9
6
0
✓
[
1
,
4
,
8
,
8
,
13
,
50
,
50
,
59
,
90
,
43
,
32
,
184
,
210
,
426
,
794
,
406
,
397
,
952
,
821
,
268
]
[1, 4, 8, 8, 13, 50, 50, 59, 90, 43, 32, 184, 210, 426, 794, 406, 397, 952, 821, 268]
[
1
,
4
,
8
,
8
,
1
3
,
5
0
,
5
0
,
5
9
,
9
0
,
4
3
,
3
2
,
1
8
4
,
2
1
0
,
4
2
6
,
7
9
4
,
4
0
6
,
3
9
7
,
9
5
2
,
8
2
1
,
2
6
8
]
Download
displayed columns
for
results
to
Text
Pari/GP
SageMath
Magma
Oscar
CSV