Properties

Base field \(\Q(\sqrt{33}) \)
Label 2.2.33.1-12.1-b
Conductor 12.1
Rank not recorded

Related objects

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Base field \(\Q(\sqrt{33}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 8 \); class number \(1\).

Elliptic curves in class 12.1-b over \(\Q(\sqrt{33}) \)

Isogeny class 12.1-b contains 12 curves linked by isogenies of degrees dividing 36.

Curve label Weierstrass Coefficients
12.1-b1 \( \bigl[1\) , \( 0\) , \( a + 1\) , \( -23 a - 171\) , \( -182 a - 930\bigr] \)
12.1-b2 \( \bigl[1\) , \( 0\) , \( a + 1\) , \( -23 a - 66\) , \( 133 a + 330\bigr] \)
12.1-b3 \( \bigl[1\) , \( 0\) , \( a + 1\) , \( 2 a + 4\) , \( -2 a - 6\bigr] \)
12.1-b4 \( \bigl[1\) , \( a + 1\) , \( 0\) , \( 27 a - 84\) , \( -63 a + 216\bigr] \)
12.1-b5 \( \bigl[1\) , \( a + 1\) , \( 0\) , \( 28022 a - 94494\) , \( -4337718 a + 14628006\bigr] \)
12.1-b6 \( \bigl[1\) , \( a + 1\) , \( 0\) , \( -4468 a - 10599\) , \( -277078 a - 657307\bigr] \)
12.1-b7 \( \bigl[1\) , \( a + 1\) , \( 0\) , \( -533 a - 1264\) , \( 10417 a + 24712\bigr] \)
12.1-b8 \( \bigl[1\) , \( a + 1\) , \( 0\) , \( 347 a - 1164\) , \( -6063 a + 20448\bigr] \)
12.1-b9 \( \bigl[1\) , \( a + 1\) , \( 0\) , \( 1752 a - 5904\) , \( -68268 a + 230220\bigr] \)
12.1-b10 \( \bigl[1\) , \( a + 1\) , \( 0\) , \( 1062 a - 3579\) , \( 31512 a - 106275\bigr] \)
12.1-b11 \( \bigl[1\) , \( a + 1\) , \( 0\) , \( -43108 a - 102264\) , \( 8190752 a + 19430768\bigr] \)
12.1-b12 \( \bigl[1\) , \( a + 1\) , \( 0\) , \( 1112 a - 3819\) , \( 27462 a - 92979\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

\(\left(\begin{array}{rrrrrrrrrrrr} 1 & 9 & 3 & 6 & 36 & 4 & 12 & 12 & 18 & 2 & 36 & 4 \\ 9 & 1 & 3 & 6 & 4 & 36 & 12 & 12 & 2 & 18 & 4 & 36 \\ 3 & 3 & 1 & 2 & 12 & 12 & 4 & 4 & 6 & 6 & 12 & 12 \\ 6 & 6 & 2 & 1 & 6 & 6 & 2 & 2 & 3 & 3 & 6 & 6 \\ 36 & 4 & 12 & 6 & 1 & 36 & 12 & 3 & 2 & 18 & 4 & 9 \\ 4 & 36 & 12 & 6 & 36 & 1 & 3 & 12 & 18 & 2 & 9 & 4 \\ 12 & 12 & 4 & 2 & 12 & 3 & 1 & 4 & 6 & 6 & 3 & 12 \\ 12 & 12 & 4 & 2 & 3 & 12 & 4 & 1 & 6 & 6 & 12 & 3 \\ 18 & 2 & 6 & 3 & 2 & 18 & 6 & 6 & 1 & 9 & 2 & 18 \\ 2 & 18 & 6 & 3 & 18 & 2 & 6 & 6 & 9 & 1 & 18 & 2 \\ 36 & 4 & 12 & 6 & 4 & 9 & 3 & 12 & 2 & 18 & 1 & 36 \\ 4 & 36 & 12 & 6 & 9 & 4 & 12 & 3 & 18 & 2 & 36 & 1 \end{array}\right)\)

Isogeny graph