Properties

Base field \(\Q(\sqrt{6}) \)
Label 2.2.24.1-48.1-a
Conductor 48.1
Rank \( 0 \)

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

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

Elliptic curves in class 48.1-a over \(\Q(\sqrt{6}) \)

Isogeny class 48.1-a contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
48.1-a1 \( \bigl[a\) , \( 1\) , \( 0\) , \( 6\) , \( -18\bigr] \)
48.1-a2 \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -14 a + 35\) , \( -67 a + 164\bigr] \)
48.1-a3 \( \bigl[a\) , \( 1\) , \( 0\) , \( 1\) , \( 0\bigr] \)
48.1-a4 \( \bigl[a\) , \( 1\) , \( 0\) , \( -4\) , \( -10\bigr] \)
48.1-a5 \( \bigl[a\) , \( 1\) , \( 0\) , \( -14\) , \( 12\bigr] \)
48.1-a6 \( \bigl[a\) , \( 1\) , \( 0\) , \( -94\) , \( -442\bigr] \)

Rank

Rank: \( 0 \)

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