Properties

Base field \(\Q(\sqrt{6}) \)
Label 2.2.24.1-256.1-f
Conductor 256.1
Rank not recorded

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Base field \(\Q(\sqrt{6}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 6 \); class number \(1\).

Elliptic curves in class 256.1-f over \(\Q(\sqrt{6}) \)

Isogeny class 256.1-f contains 4 curves linked by isogenies of degrees dividing 6.

Curve label Weierstrass Coefficients
256.1-f1 \( \bigl[0\) , \( -a\) , \( 0\) , \( 2\) , \( a - 3\bigr] \)
256.1-f2 \( \bigl[0\) , \( -a\) , \( 0\) , \( 2\) , \( a + 3\bigr] \)
256.1-f3 \( \bigl[0\) , \( -a\) , \( 0\) , \( -10 a - 23\) , \( 35 a + 86\bigr] \)
256.1-f4 \( \bigl[0\) , \( -a\) , \( 0\) , \( 10 a - 23\) , \( 35 a - 86\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph