Properties

Base field \(\Q(\sqrt{6}) \)
Label 2.2.24.1-400.1-a
Conductor 400.1
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 400.1-a over \(\Q(\sqrt{6}) \)

Isogeny class 400.1-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label Weierstrass Coefficients
400.1-a1 \( \bigl[a\) , \( -1\) , \( a\) , \( -12\) , \( -19\bigr] \)
400.1-a2 \( \bigl[a\) , \( -1\) , \( a\) , \( -2\) , \( -1\bigr] \)
400.1-a3 \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -26 a - 63\) , \( 111 a + 272\bigr] \)
400.1-a4 \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -826 a - 2023\) , \( -19297 a - 47268\bigr] \)

Rank

Rank: \( 0 \)

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