Properties

Base field \(\Q(\sqrt{3}) \)
Label 2.2.12.1-3072.1-f
Conductor 3072.1
Rank \( 1 \)

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 3072.1-f over \(\Q(\sqrt{3}) \)

Isogeny class 3072.1-f contains 8 curves linked by isogenies of degrees dividing 16.

Curve label Weierstrass Coefficients
3072.1-f1 \( \bigl[0\) , \( -1\) , \( 0\) , \( 30890 a - 53505\) , \( 3879118 a - 6718827\bigr] \)
3072.1-f2 \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 32 a + 64\) , \( -1080 a - 1800\bigr] \)
3072.1-f3 \( \bigl[0\) , \( a - 1\) , \( 0\) , \( -3882 a + 6724\) , \( 217892 a - 377400\bigr] \)
3072.1-f4 \( \bigl[0\) , \( -1\) , \( 0\) , \( 130 a - 225\) , \( 750 a - 1299\bigr] \)
3072.1-f5 \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -48 a - 96\) , \( -216 a - 360\bigr] \)
3072.1-f6 \( \bigl[0\) , \( -1\) , \( 0\) , \( 1930 a - 3345\) , \( 60126 a - 104139\bigr] \)
3072.1-f7 \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -768 a - 1536\) , \( -16632 a - 27720\bigr] \)
3072.1-f8 \( \bigl[0\) , \( -1\) , \( 0\) , \( 1770 a - 3105\) , \( 69998 a - 121131\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph