Curve name | X100a | |||||||||
Index | 48 | |||||||||
Level | 8 | |||||||||
Genus | 0 | |||||||||
Does the subgroup contain −I? | No | |||||||||
Generating matrices | [1247],[1203],[7607],[3647] | |||||||||
Images in lower levels |
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Meaning/Special name | ||||||||||
Chosen covering | X100 | |||||||||
Curves that X100a minimally covers | ||||||||||
Curves that minimally cover X100a | ||||||||||
Curves that minimally cover X100a 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)=−27t16+324t12−1728t8+5184t4−6912 B(t)=54t24−972t20+5184t16−82944t8+248832t4−221184 | |||||||||
Info about rational points | ||||||||||
Comments on finding rational points | None | |||||||||
Elliptic curve whose 2-adic image is the subgroup | y2=x3−x2−12358012x+16581170740, with conductor 142296 | |||||||||
Generic density of odd order reductions | 307/2688 |