Properties

Base field \(\Q(\sqrt{3}) \)
Label 2.2.12.1-162.1-a
Conductor 162.1
Rank not recorded

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Base field \(\Q(\sqrt{3}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 3 \); class number \(1\).

Elliptic curves in class 162.1-a over \(\Q(\sqrt{3}) \)

Isogeny class 162.1-a contains 3 curves linked by isogenies of degrees dividing 9.

Curve label Weierstrass Coefficients
162.1-a1 \( \bigl[a\) , \( 0\) , \( 0\) , \( -3\) , \( -3\bigr] \)
162.1-a2 \( \bigl[1\) , \( -1\) , \( 1\) , \( -14\) , \( 29\bigr] \)
162.1-a3 \( \bigl[1\) , \( -1\) , \( 1\) , \( 1\) , \( -1\bigr] \)

Rank

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Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)

Isogeny graph