Curve name | X67d | |||||||||
Index | 48 | |||||||||
Level | 8 | |||||||||
Genus | 0 | |||||||||
Does the subgroup contain −I? | No | |||||||||
Generating matrices | [3005],[3047],[3663] | |||||||||
Images in lower levels |
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Meaning/Special name | ||||||||||
Chosen covering | X67 | |||||||||
Curves that X67d minimally covers | ||||||||||
Curves that minimally cover X67d | ||||||||||
Curves that minimally cover X67d 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)=−108t16−1296t12−6912t8−20736t4−27648 B(t)=432t24+7776t20+41472t16−663552t8−1990656t4−1769472 | |||||||||
Info about rational points | ||||||||||
Comments on finding rational points | None | |||||||||
Elliptic curve whose 2-adic image is the subgroup | y2=x3−700x−6000, with conductor 1600 | |||||||||
Generic density of odd order reductions | 419/2688 |