Properties

Base field \(\Q(\sqrt{6}) \)
Label 2.2.24.1-200.1-a
Conductor 200.1
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 200.1-a over \(\Q(\sqrt{6}) \)

Isogeny class 200.1-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
200.1-a1 \( \bigl[a\) , \( 0\) , \( a\) , \( 65 a + 157\) , \( -809 a - 1983\bigr] \)
200.1-a2 \( \bigl[a\) , \( 0\) , \( a\) , \( -35 a - 88\) , \( -166 a - 408\bigr] \)
200.1-a3 \( \bigl[0\) , \( 0\) , \( 0\) , \( -2\) , \( 1\bigr] \)
200.1-a4 \( \bigl[a\) , \( 0\) , \( a\) , \( 535 a - 1313\) , \( 10811 a - 26483\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

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

Isogeny graph