Curve name | X192h | ||||||||||||
Index | 96 | ||||||||||||
Level | 16 | ||||||||||||
Genus | 0 | ||||||||||||
Does the subgroup contain −I? | No | ||||||||||||
Generating matrices | [9001],[71405],[1205],[9087],[1005] | ||||||||||||
Images in lower levels |
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Meaning/Special name | |||||||||||||
Chosen covering | X192 | ||||||||||||
Curves that X192h minimally covers | |||||||||||||
Curves that minimally cover X192h | |||||||||||||
Curves that minimally cover X192h 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)=−27t24−23760t22+870048t20+2025216t18−276804864t16+1757306880t14−6309494784t12+28116910080t10−70862045184t8+8295284736t6+57019465728t4−24914165760t2−452984832 B(t)=54t36−115344t34−1858464t32+510879744t30−15214086144t28+140525715456t26−307830620160t24+7470640005120t22−110151479328768t20+632942965555200t18−1762423669260288t16+1912483841310720t14−1260874220175360t12+9209493288124416t10−15953125592530944t8+8571139815112704t6−498877631299584t4−495398707789824t2+3710851743744 | ||||||||||||
Info about rational points | |||||||||||||
Comments on finding rational points | None | ||||||||||||
Elliptic curve whose 2-adic image is the subgroup | y2+xy+y=x3+x2−5882451x+5488977549, with conductor 1470 | ||||||||||||
Generic density of odd order reductions | 11/112 |