| dc.creator |
Propp, Oron Y |
|
| dc.date |
2021-09-20T17:17:13Z |
|
| dc.date |
2021-09-20T17:17:13Z |
|
| dc.date |
2018-02-20 |
|
| dc.date |
2020-09-24T21:18:22Z |
|
| dc.date.accessioned |
2023-03-01T18:10:37Z |
|
| dc.date.available |
2023-03-01T18:10:37Z |
|
| dc.identifier |
https://hdl.handle.net/1721.1/131476 |
|
| dc.identifier |
Research in Number Theory. 2018 Feb 20;4(1):12 |
|
| dc.identifier.uri |
http://localhost:8080/xmlui/handle/CUHPOERS/279038 |
|
| dc.description |
Abstract
Let
$$\ell $$
ℓ
be an odd prime and d a positive integer. We determine when there exists a degree-d number field K and an elliptic curve E / K with
$$j(E)\in \mathbb {Q}\setminus \{0,1728\}$$
j
(
E
)
∈
Q
\
{
0
,
1728
}
for which
$$E(K)_\mathrm {tors}$$
E
(
K
)
tors
contains a point of order
$$\ell $$
ℓ
, conditionally on a conjecture of Sutherland. We likewise determine when there exists such a pair (K, E) for which the image of the associated mod-
$$\ell $$
ℓ
Galois representation is contained in a Cartan subgroup or its normalizer. We do the same under the stronger assumption that E is defined over
$$\mathbb {Q}$$
Q
. |
|
| dc.format |
application/pdf |
|
| dc.language |
en |
|
| dc.publisher |
Springer International Publishing |
|
| dc.relation |
https://doi.org/10.1007/s40993-018-0097-y |
|
| dc.rights |
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. |
|
| dc.rights |
SpringerNature |
|
| dc.source |
Springer International Publishing |
|
| dc.title |
Cartan images and $$\ell $$ ℓ -torsion points of elliptic curves with rational j-invariant |
|
| dc.type |
Article |
|
| dc.type |
http://purl.org/eprint/type/JournalArticle |
|