Properties

Base field \(\Q(\sqrt{3}) \)
Label 2.2.12.1-16.1-a
Conductor 16.1
Rank \( 0 \)

Related objects

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Base field \(\Q(\sqrt{3}) \)

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

Elliptic curves in class 16.1-a over \(\Q(\sqrt{3}) \)

Isogeny class 16.1-a contains 8 curves linked by isogenies of degrees dividing 12.

Curve label Weierstrass Coefficients
16.1-a1 \( \bigl[0\) , \( -a\) , \( 0\) , \( 1\) , \( -3 a - 5\bigr] \)
16.1-a2 \( \bigl[0\) , \( a\) , \( 0\) , \( 1\) , \( 3 a + 5\bigr] \)
16.1-a3 \( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 4 a - 13\) , \( 11 a - 21\bigr] \)
16.1-a4 \( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 4 a - 13\) , \( -12 a + 19\bigr] \)
16.1-a5 \( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -a - 3\) , \( -1\bigr] \)
16.1-a6 \( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -a - 3\) , \( -a - 1\bigr] \)
16.1-a7 \( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -6 a - 13\) , \( -12 a - 21\bigr] \)
16.1-a8 \( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -6 a - 13\) , \( 11 a + 19\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 3 & 12 & 4 & 6 & 2 & 4 & 12 \\ 3 & 1 & 4 & 12 & 2 & 6 & 12 & 4 \\ 12 & 4 & 1 & 12 & 2 & 6 & 3 & 4 \\ 4 & 12 & 12 & 1 & 6 & 2 & 4 & 3 \\ 6 & 2 & 2 & 6 & 1 & 3 & 6 & 2 \\ 2 & 6 & 6 & 2 & 3 & 1 & 2 & 6 \\ 4 & 12 & 3 & 4 & 6 & 2 & 1 & 12 \\ 12 & 4 & 4 & 3 & 2 & 6 & 12 & 1 \end{array}\right)\)

Isogeny graph