Properties

Base field \(\Q(\sqrt{3}) \)
Label 2.2.12.1-3072.1-b
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-b over \(\Q(\sqrt{3}) \)

Isogeny class 3072.1-b contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
3072.1-b1 \( \bigl[0\) , \( a - 1\) , \( 0\) , \( -48 a - 112\) , \( 1016 a + 1720\bigr] \)
3072.1-b2 \( \bigl[0\) , \( -1\) , \( 0\) , \( 107702 a - 186545\) , \( -25356654 a + 43919013\bigr] \)
3072.1-b3 \( \bigl[0\) , \( -1\) , \( 0\) , \( 6862 a - 11885\) , \( -381770 a + 661245\bigr] \)
3072.1-b4 \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -23148 a + 40096\) , \( -10988976 a + 19033464\bigr] \)
3072.1-b5 \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 116 a - 200\) , \( 756 a - 1308\bigr] \)
3072.1-b6 \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -244 a + 400\) , \( 4260 a - 7308\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph