Timeline for Conductor of hyperelliptic curve after adding a rational root
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 14 at 19:39 | comment | added | Aurel | Indeed, it might be that there is no conductor drop in your family. | |
| Jul 13 at 17:39 | comment | added | Maleeha | Thanks for your comment! I'm considering a fixed family of hyperelliptic curves - I think this is not necessarily the case in general? | |
| Jul 11 at 14:19 | comment | added | Aurel | At a glance it looks like the mod 2 representation will be related (maybe the same?). In many cases the conductor of the curve at odd primes is the same as that of the mod 2 representation, so that should explain your observation. On the other hand, they sometimes differ (there is a conductor drop from the 2-adic to the mod 2 representation) in which case your observation might not hold. So maybe a counter-example exists; how hard have you tried to look for one? | |
| Jul 4 at 12:19 | history | asked | Maleeha | CC BY-SA 4.0 |