Properties

Base field \(\Q(\sqrt{3}) \)
Label 2.2.12.1-726.1-h
Conductor 726.1
Rank not recorded

Related objects

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

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

Elliptic curves in class 726.1-h over \(\Q(\sqrt{3}) \)

Isogeny class 726.1-h contains 4 curves linked by isogenies of degrees dividing 6.

Curve label Weierstrass Coefficients
726.1-h1 \( \bigl[1\) , \( 0\) , \( 1\) , \( -41\) , \( -556\bigr] \)
726.1-h2 \( \bigl[1\) , \( 0\) , \( 1\) , \( 4\) , \( 20\bigr] \)
726.1-h3 \( \bigl[1\) , \( 0\) , \( 1\) , \( -6\) , \( 4\bigr] \)
726.1-h4 \( \bigl[1\) , \( 0\) , \( 1\) , \( -81\) , \( -284\bigr] \)

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