Properties

Base field \(\Q(\sqrt{3}) \)
Label 2.2.12.1-768.1-a
Conductor 768.1
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 768.1-a over \(\Q(\sqrt{3}) \)

Isogeny class 768.1-a contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
768.1-a1 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 1354602 a - 2346237\) , \( -1124664415 a + 1947975909\bigr] \)
768.1-a2 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 36546 a - 63297\) , \( 4995933 a - 8653209\bigr] \)
768.1-a3 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 2286 a - 3957\) , \( 77553 a - 134325\bigr] \)
768.1-a4 \( \bigl[0\) , \( 1\) , \( 0\) , \( 37894 a - 65634\) , \( 667716 a - 1156518\bigr] \)
768.1-a5 \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -10 a - 41\) , \( 11 a - 177\bigr] \)
768.1-a6 \( \bigl[0\) , \( 1\) , \( 0\) , \( -150276 a + 260286\) , \( 5169562 a - 8953944\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph