Properties

Base field \(\Q(\sqrt{6}) \)
Label 2.2.24.1-600.1-o
Conductor 600.1
Rank \( 1 \)

Related objects

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

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

Elliptic curves in class 600.1-o over \(\Q(\sqrt{6}) \)

Isogeny class 600.1-o contains 8 curves linked by isogenies of degrees dividing 16.

Curve label Weierstrass Coefficients
600.1-o1 \( \bigl[a\) , \( 1\) , \( a\) , \( 2450 a - 6801\) , \( -109970 a + 277443\bigr] \)
600.1-o2 \( \bigl[a\) , \( 1\) , \( a\) , \( -21\) , \( 279\bigr] \)
600.1-o3 \( \bigl[a\) , \( 1\) , \( a\) , \( 19\) , \( 9\bigr] \)
600.1-o4 \( \bigl[a\) , \( 1\) , \( a\) , \( -6\) , \( -6\bigr] \)
600.1-o5 \( \bigl[a\) , \( 1\) , \( a\) , \( -51\) , \( 93\bigr] \)
600.1-o6 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -306 a - 749\) , \( -4921 a - 12054\bigr] \)
600.1-o7 \( \bigl[a\) , \( 1\) , \( a\) , \( -801\) , \( 8043\bigr] \)
600.1-o8 \( \bigl[a\) , \( 1\) , \( a\) , \( -2450 a - 6801\) , \( 109970 a + 277443\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 8 & 16 & 8 & 4 & 16 & 2 & 4 \\ 8 & 1 & 8 & 4 & 2 & 8 & 4 & 8 \\ 16 & 8 & 1 & 2 & 4 & 4 & 8 & 16 \\ 8 & 4 & 2 & 1 & 2 & 2 & 4 & 8 \\ 4 & 2 & 4 & 2 & 1 & 4 & 2 & 4 \\ 16 & 8 & 4 & 2 & 4 & 1 & 8 & 16 \\ 2 & 4 & 8 & 4 & 2 & 8 & 1 & 2 \\ 4 & 8 & 16 & 8 & 4 & 16 & 2 & 1 \end{array}\right)\)

Isogeny graph