Properties

Base field 3.3.316.1
Label 3.3.316.1-22.2-b
Conductor 22.2
Rank \( 0 \)

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Base field 3.3.316.1

Generator \(a\), with minimal polynomial \( x^{3} - x^{2} - 4 x + 2 \); class number \(1\).

Elliptic curves in class 22.2-b over 3.3.316.1

Isogeny class 22.2-b contains 8 curves linked by isogenies of degrees dividing 16.

Curve label Weierstrass Coefficients
22.2-b1 \( \bigl[1\) , \( a^{2} + a - 3\) , \( 1\) , \( 2 a^{2} + 3 a - 1\) , \( 3 a^{2} + 4 a - 3\bigr] \)
22.2-b2 \( \bigl[1\) , \( a^{2} - a - 2\) , \( 0\) , \( 17779103255 a^{2} - 9410775234 a - 75545910366\) , \( -1887000315351215 a^{2} + 998820553693101 a + 8018129535547874\bigr] \)
22.2-b3 \( \bigl[1\) , \( a^{2} - a - 2\) , \( 0\) , \( 1111193215 a^{2} - 588174489 a - 4721618846\) , \( -29484933946309 a^{2} + 15606864446438 a + 125285628176318\bigr] \)
22.2-b4 \( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( 157165 a^{2} - 87989 a - 676517\) , \( 50605254 a^{2} - 27049557 a - 215506463\bigr] \)
22.2-b5 \( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( 12455 a^{2} - 6894 a - 53467\) , \( 338649 a^{2} - 183469 a - 1446615\bigr] \)
22.2-b6 \( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( 7180 a^{2} - 3834 a - 30567\) , \( -482724 a^{2} + 255539 a + 2051207\bigr] \)
22.2-b7 \( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( -47855 a^{2} + 25241 a + 203183\) , \( 2667776 a^{2} - 1421813 a - 11353375\bigr] \)
22.2-b8 \( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( 10722567238754 a^{2} - 5675632707869 a - 45561695284518\) , \( -28176030177448107125 a^{2} + 14914039935153923948 a + 119723912030592754237\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 8 & 4 & 8 & 4 & 2 & 8 & 8 \\ 8 & 1 & 2 & 16 & 8 & 4 & 16 & 4 \\ 4 & 2 & 1 & 8 & 4 & 2 & 8 & 2 \\ 8 & 16 & 8 & 1 & 2 & 4 & 4 & 16 \\ 4 & 8 & 4 & 2 & 1 & 2 & 2 & 8 \\ 2 & 4 & 2 & 4 & 2 & 1 & 4 & 4 \\ 8 & 16 & 8 & 4 & 2 & 4 & 1 & 16 \\ 8 & 4 & 2 & 16 & 8 & 4 & 16 & 1 \end{array}\right)\)

Isogeny graph