Properties

Base field \(\Q(\sqrt{3}) \)
Label 2.2.12.1-192.1-a
Conductor 192.1
Rank not recorded

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

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

Elliptic curves in class 192.1-a over \(\Q(\sqrt{3}) \)

Isogeny class 192.1-a contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
192.1-a1 \( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 5 a - 8\) , \( 5 a - 10\bigr] \)
192.1-a2 \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -8 a + 14\) , \( -15 a + 26\bigr] \)
192.1-a3 \( \bigl[0\) , \( 1\) , \( 0\) , \( -2\) , \( 0\bigr] \)
192.1-a4 \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -18 a - 29\) , \( -47 a - 81\bigr] \)
192.1-a5 \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 31 a - 58\) , \( -113 a + 194\bigr] \)
192.1-a6 \( \bigl[a + 1\) , \( a\) , \( 0\) , \( -4 a - 6\) , \( -13 a - 24\bigr] \)

Rank

Rank not yet determined.

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