Curve name | X84j | |||||||||
Index | 48 | |||||||||
Level | 8 | |||||||||
Genus | 0 | |||||||||
Does the subgroup contain −I? | No | |||||||||
Generating matrices | [5505],[7703],[1003] | |||||||||
Images in lower levels |
|
|||||||||
Meaning/Special name | ||||||||||
Chosen covering | X84 | |||||||||
Curves that X84j minimally covers | ||||||||||
Curves that minimally cover X84j | ||||||||||
Curves that minimally cover X84j and have infinitely many rational points. | ||||||||||
Model | P1, a universal elliptic curve over an appropriate base is given by y2=x3+A(t)x+B(t), where A(t)=−108t8−432t6+1080t4+3024t2−108 B(t)=432t12+2592t10+19440t8+60480t6+42768t4−28512t2−432 | |||||||||
Info about rational points | ||||||||||
Comments on finding rational points | None | |||||||||
Elliptic curve whose 2-adic image is the subgroup | y2=x3+x2−321x+18879, with conductor 960 | |||||||||
Generic density of odd order reductions | 635/5376 |