Curve name | X226 | ||||||||||||
Index | 48 | ||||||||||||
Level | 16 | ||||||||||||
Genus | 0 | ||||||||||||
Does the subgroup contain −I? | Yes | ||||||||||||
Generating matrices | [3603],[9941],[15001],[3003] | ||||||||||||
Images in lower levels |
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Meaning/Special name | |||||||||||||
Chosen covering | X79 | ||||||||||||
Curves that X226 minimally covers | X79 | ||||||||||||
Curves that minimally cover X226 | X226a, X226b, X226c, X226d, X226e, X226f, X226g, X226h | ||||||||||||
Curves that minimally cover X226 and have infinitely many rational points. | X226a, X226b, X226c, X226d, X226e, X226f, X226g, X226h | ||||||||||||
Model | P1,Q(X226)=Q(f226),f79=4f226+4f2226−2 | ||||||||||||
Info about rational points | None | ||||||||||||
Comments on finding rational points | None | ||||||||||||
Elliptic curve whose 2-adic image is the subgroup | y2=x3−55862675x+151569825750, with conductor 421600 | ||||||||||||
Generic density of odd order reductions | 9249/57344 |