Properties

Base field \(\Q(\sqrt{6}) \)
Label 2.2.24.1-588.1-d
Conductor 588.1
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 588.1-d over \(\Q(\sqrt{6}) \)

Isogeny class 588.1-d contains 4 curves linked by isogenies of degrees dividing 6.

Curve label Weierstrass Coefficients
588.1-d1 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -2266 a - 5551\) , \( 92089 a + 225572\bigr] \)
588.1-d2 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 134 a + 329\) , \( 601 a + 1472\bigr] \)
588.1-d3 \( \bigl[a\) , \( 1\) , \( 0\) , \( -5\) , \( -3\bigr] \)
588.1-d4 \( \bigl[a\) , \( 1\) , \( 0\) , \( -455\) , \( 3381\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph