Properties

Base field \(\Q(\sqrt{33}) \)
Label 2.2.33.1-12.1-a
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-a over \(\Q(\sqrt{33}) \)

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

Curve label Weierstrass Coefficients
12.1-a1 \( \bigl[1\) , \( -a - 1\) , \( 1\) , \( 43110 a - 145374\) , \( -8233861 a + 27766893\bigr] \)
12.1-a2 \( \bigl[1\) , \( -a - 1\) , \( 1\) , \( 4470 a - 15069\) , \( 272609 a - 919317\bigr] \)
12.1-a3 \( \bigl[1\) , \( -a - 1\) , \( 1\) , \( 535 a - 1799\) , \( -10951 a + 36927\bigr] \)
12.1-a4 \( \bigl[1\) , \( -a - 1\) , \( 1\) , \( -25 a - 59\) , \( 89 a + 211\bigr] \)
12.1-a5 \( \bigl[1\) , \( -a - 1\) , \( 1\) , \( -1110 a - 2709\) , \( -26351 a - 62809\bigr] \)
12.1-a6 \( \bigl[1\) , \( 0\) , \( a\) , \( 22 a - 88\) , \( -134 a + 464\bigr] \)
12.1-a7 \( \bigl[1\) , \( 0\) , \( a\) , \( -3 a + 7\) , \( a - 7\bigr] \)
12.1-a8 \( \bigl[1\) , \( -a - 1\) , \( 1\) , \( -345 a - 819\) , \( 6409 a + 15203\bigr] \)
12.1-a9 \( \bigl[1\) , \( -a - 1\) , \( 1\) , \( -1060 a - 2519\) , \( -30451 a - 72245\bigr] \)
12.1-a10 \( \bigl[1\) , \( -a - 1\) , \( 1\) , \( -1750 a - 4154\) , \( 70019 a + 166105\bigr] \)
12.1-a11 \( \bigl[1\) , \( 0\) , \( a\) , \( 22 a - 193\) , \( 181 a - 1111\bigr] \)
12.1-a12 \( \bigl[1\) , \( -a - 1\) , \( 1\) , \( -28020 a - 66474\) , \( 4365739 a + 10356761\bigr] \)

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