forked from JohnCremona/eclib
-
Notifications
You must be signed in to change notification settings - Fork 0
/
tcurve.out
64 lines (60 loc) · 1.4 KB
/
tcurve.out
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
Enter a curve:
The curve is [0,0,1,-7,6]
A test of invariants:
The curve is [0,0,1,-7,6]
b2 = 0 b4 = -14 b6 = 25 b8 = -49
c4 = 336 c6 = -5400
disc = 5077 (# real components = 2)
#torsion not yet computed
The minimal curve is [0,0,1,-7,6] (reduced minimal model)
b2 = 0 b4 = -14 b6 = 25 b8 = -49
c4 = 336 c6 = -5400
disc = 5077 (# real components = 2)
#torsion not yet computed
A test of Tate's algorithm:
[0,0,1,-7,6] (reduced minimal model)
b2 = 0 b4 = -14 b6 = 25 b8 = -49
c4 = 336 c6 = -5400
disc = 5077 (bad primes: [ 5077 ]; # real components = 2)
#torsion not yet computed
Conductor = 5077
Full display:
[0,0,1,-7,6] (reduced minimal model)
b2 = 0 b4 = -14 b6 = 25 b8 = -49
c4 = 336 c6 = -5400
disc = 5077 (bad primes: [ 5077 ]; # real components = 2)
#torsion not yet computed
Conductor = 5077
Global Root Number = -1
Reduction type at bad primes:
p ord(d) ord(N) ord(j) Kodaira c_p root_number
5077 1 1 1 I1 1 1
Traces of Frobenius:
p=2: ap=-2
p=3: ap=-3
p=5: ap=-4
p=7: ap=-4
p=11: ap=-6
p=13: ap=-4
p=17: ap=-4
p=19: ap=-7
p=23: ap=-6
p=29: ap=-6
p=31: ap=-2
p=37: ap=0
p=41: ap=0
p=43: ap=-8
p=47: ap=-9
p=53: ap=-9
p=59: ap=-11
p=61: ap=-2
p=67: ap=-12
p=71: ap=-8
p=73: ap=-14
p=79: ap=9
p=83: ap=-2
p=89: ap=11
p=97: ap=6
Testing construction from a non-integral model:
After scaling down by 60, coeffs are [0,0,1/216000,-7/12960000,1/7776000000]
Constructed curve is [0,0,1,-7,6] with scale = 60