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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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✓ 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.216.95a
1
1
1
6
6
6
1
1
1
U
(
1
)
3
\mathrm{U}(1)_{3}
U
(
1
)
3
J
s
(
C
(
6
,
6
)
)
J_s(C(6,6))
J
s
(
C
(
6
,
6
)
)
216
216
2
1
6
91
/
108
91/108
9
1
/
1
0
8
1
1
1
15
15
1
5
310
310
3
1
0
7455
7455
7
4
5
5
195426
195426
1
9
5
4
2
6
195426
195426
1
9
5
4
2
6
1
1
1
5
5
5
34
34
3
4
317
317
3
1
7
3396
3396
3
3
9
6
39094
39094
3
9
0
9
4
6
6
6
822
822
8
2
2
184880
184880
1
8
4
8
8
0
✓
[
1
,
1
,
4
,
3
,
6
,
26
,
27
,
38
,
57
,
26
,
16
,
125
,
142
,
315
,
602
,
281
,
293
,
662
,
544
,
151
]
[1, 1, 4, 3, 6, 26, 27, 38, 57, 26, 16, 125, 142, 315, 602, 281, 293, 662, 544, 151]
[
1
,
1
,
4
,
3
,
6
,
2
6
,
2
7
,
3
8
,
5
7
,
2
6
,
1
6
,
1
2
5
,
1
4
2
,
3
1
5
,
6
0
2
,
2
8
1
,
2
9
3
,
6
6
2
,
5
4
4
,
1
5
1
]
Download
displayed columns
for
results
to
Text
Pari/GP
SageMath
Magma
Oscar
CSV