Properties

Base field \(\Q(\sqrt{6}) \)
Label 2.2.24.1-10.2-a
Conductor 10.2
Rank \( 0 \)

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Base field \(\Q(\sqrt{6}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 6 \); class number \(1\).

Elliptic curves in class 10.2-a over \(\Q(\sqrt{6}) \)

Isogeny class 10.2-a contains 3 curves linked by isogenies of degrees dividing 9.

Curve label Weierstrass Coefficients
10.2-a1 \( \bigl[1\) , \( 0\) , \( 1\) , \( 166 a - 413\) , \( -1827 a + 4480\bigr] \)
10.2-a2 \( \bigl[1\) , \( 0\) , \( 1\) , \( a - 3\) , \( -5 a + 12\bigr] \)
10.2-a3 \( \bigl[1\) , \( 0\) , \( 1\) , \( -9 a + 22\) , \( 133 a - 326\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph