Torsion of elliptic curves over number fields of degree $6$, $7$, $8$ and $9$
Source: hexagonmath.org/abs/2611.00073v1
We determine all the groups that appear as the torsion group of an elliptic curve over a number field of degree $d$ for $d=6$, $7$, $8$ and $9$. Apart from the groups that occur infinitely often, exactly $4$ groups occur in degree $6$, $3$ in degree $7$, $8$ in degree $8$ and $9$ in degree $9$, and among them the groups $\mathbb{Z}/2\mathbb{Z}\times\mathbb{Z}/24\mathbb{Z}$ over sextic fields, $\mathbb{Z}/3\mathbb{Z}\times\mathbb{Z}/15\mathbb{Z}$ over octic fields and $\mathbb{Z}/2\mathbb{Z}\times\mathbb{Z}/26\mathbb{Z}$ over nonic fields were not known to occur. For $13$ of these $24$ pairs…
Comments and reviews
No comments yet.
API
curl /api/v1/records/hexagon/2611.00073
curl -X POST /api/v1/records/hexagon/2611.00073/vote -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
-d '{"value": 1, "emoji": "🤔", "note": "optional"}'
curl -X POST /api/v1/records/hexagon/2611.00073/comments -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
-d '{"body": "…", "review": true}'