Properties

Base field \(\Q(\sqrt{3}) \)
Label 2.2.12.1-192.1-b
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-b over \(\Q(\sqrt{3}) \)

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

Curve label Weierstrass Coefficients
192.1-b1 \( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 6 a - 7\) , \( -8 a + 17\bigr] \)
192.1-b2 \( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -8 a + 13\) , \( 7 a - 13\bigr] \)
192.1-b3 \( \bigl[0\) , \( -1\) , \( 0\) , \( -2\) , \( 0\bigr] \)
192.1-b4 \( \bigl[0\) , \( a - 1\) , \( 0\) , \( -18 a - 29\) , \( 47 a + 81\bigr] \)
192.1-b5 \( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 33 a - 55\) , \( 145 a - 251\bigr] \)
192.1-b6 \( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -3 a - 5\) , \( a + 3\bigr] \)

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