Curve name | X118x | ||||||||||||
Index | 48 | ||||||||||||
Level | 16 | ||||||||||||
Genus | 0 | ||||||||||||
Does the subgroup contain −I? | No | ||||||||||||
Generating matrices | [1101],[7001],[3007],[3003] | ||||||||||||
Images in lower levels |
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Meaning/Special name | |||||||||||||
Chosen covering | X118 | ||||||||||||
Curves that X118x minimally covers | |||||||||||||
Curves that minimally cover X118x | |||||||||||||
Curves that minimally cover X118x 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)=−108t12−864t10+13824t6+25920t4−13824t2−27648 B(t)=432t18+5184t16+10368t14−96768t12−445824t10−41472t8+2515968t6+3649536t4+1327104t2+1769472 | ||||||||||||
Info about rational points | |||||||||||||
Comments on finding rational points | None | ||||||||||||
Elliptic curve whose 2-adic image is the subgroup | y2=x3−x2−21442776x+41636137776, with conductor 40560 | ||||||||||||
Generic density of odd order reductions | 41/336 |