Properties

Base field \(\Q(\sqrt{6}) \)
Label 2.2.24.1-24.1-b
Conductor 24.1
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 24.1-b over \(\Q(\sqrt{6}) \)

Isogeny class 24.1-b contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
24.1-b1 \( \bigl[a\) , \( a - 1\) , \( 0\) , \( -78 a + 194\) , \( 4376 a - 10718\bigr] \)
24.1-b2 \( \bigl[0\) , \( -1\) , \( 0\) , \( 1\) , \( 0\bigr] \)
24.1-b3 \( \bigl[a\) , \( a - 1\) , \( 0\) , \( 22 a - 51\) , \( -78 a + 192\bigr] \)
24.1-b4 \( \bigl[a\) , \( a - 1\) , \( 0\) , \( 122 a - 296\) , \( 1012 a - 2478\bigr] \)
24.1-b5 \( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -322 a - 786\) , \( 5124 a + 12552\bigr] \)
24.1-b6 \( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -1922 a - 4706\) , \( -70528 a - 172758\bigr] \)

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