Properties

Base field \(\Q(\sqrt{6}) \)
Label 2.2.24.1-726.1-c
Conductor 726.1
Rank \( 0 \)

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 726.1-c over \(\Q(\sqrt{6}) \)

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

Curve label Weierstrass Coefficients
726.1-c1 \( \bigl[1\) , \( 1\) , \( 1\) , \( -12\) , \( -81\bigr] \)
726.1-c2 \( \bigl[1\) , \( 1\) , \( 1\) , \( -2\) , \( -1\bigr] \)
726.1-c3 \( \bigl[1\) , \( 1\) , \( 1\) , \( -22\) , \( -49\bigr] \)
726.1-c4 \( \bigl[1\) , \( 1\) , \( 1\) , \( -352\) , \( -2689\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph