Properties

Base field \(\Q(\sqrt{6}) \)
Label 2.2.24.1-96.1-b
Conductor 96.1
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 96.1-b over \(\Q(\sqrt{6}) \)

Isogeny class 96.1-b contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
96.1-b1 \( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -137 a - 334\) , \( -2216 a - 5429\bigr] \)
96.1-b2 \( \bigl[a\) , \( a - 1\) , \( a\) , \( -38 a + 93\) , \( 159 a - 390\bigr] \)
96.1-b3 \( \bigl[0\) , \( -1\) , \( 0\) , \( -2\) , \( 0\bigr] \)
96.1-b4 \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -86 a - 210\) , \( 774 a + 1896\bigr] \)
96.1-b5 \( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -162 a - 394\) , \( -1646 a - 4031\bigr] \)
96.1-b6 \( \bigl[a\) , \( a - 1\) , \( 0\) , \( 137 a - 334\) , \( 2216 a - 5429\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

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

Isogeny graph