Curve name |
X677 |
Index |
96 |
Level |
32 |
Genus |
5 |
Does the subgroup contain −I? |
Yes |
Generating matrices |
[25081],[23501],[131323],[111101] |
Images in lower levels |
Level | Index of image | Corresponding curve |
2 |
3 |
X6 |
4 |
6 |
X11 |
8 |
24 |
X91 |
16 |
48 |
X291 |
|
Meaning/Special name |
|
Chosen covering |
X291 |
Curves that X677 minimally covers |
X291 |
Curves that minimally cover X677 |
|
Curves that minimally cover X677 and have infinitely many rational
points. |
|
Model |
y2=x3−2xw2=4x2y−4xy−y3 |
Info about rational points |
Rational point | Image on the j-line |
(0:0:1:0) |
Singular
|
(0:0:0:1) |
Singular
|
|
Comments on finding rational points |
This curve admits a family of twists of etale double covers that are also
modular curves. Each of these modular curves maps to one we have already
computed that has finitely many rational points. |
Elliptic curve whose 2-adic image is the subgroup |
None |
Generic density of odd order reductions |
N/A |