Properties

Base field \(\Q(\sqrt{-2}) \)
Label 2.0.8.1-6912.3-a
Conductor 6912.3
Rank \( 1 \)

Related objects

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Base field \(\Q(\sqrt{-2}) \)

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

Elliptic curves in class 6912.3-a over \(\Q(\sqrt{-2}) \)

Isogeny class 6912.3-a contains 8 curves linked by isogenies of degrees dividing 16.

Curve label Weierstrass Coefficients
6912.3-a1 \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -32 a - 16\) , \( -180 a - 900\bigr] \)
6912.3-a2 \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -2 a - 1\) , \( 0\bigr] \)
6912.3-a3 \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 8 a + 4\) , \( 4 a + 20\bigr] \)
6912.3-a4 \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 48 a + 24\) , \( -36 a - 180\bigr] \)
6912.3-a5 \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -952 a + 784\) , \( -548 a - 23908\bigr] \)
6912.3-a6 \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -392 a - 1456\) , \( -8388 a - 20772\bigr] \)
6912.3-a7 \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 128 a + 64\) , \( 220 a + 1100\bigr] \)
6912.3-a8 \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 768 a + 384\) , \( -2772 a - 13860\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 8 & 4 & 2 & 2 & 2 & 8 & 4 \\ 8 & 1 & 2 & 4 & 16 & 16 & 4 & 8 \\ 4 & 2 & 1 & 2 & 8 & 8 & 2 & 4 \\ 2 & 4 & 2 & 1 & 4 & 4 & 4 & 2 \\ 2 & 16 & 8 & 4 & 1 & 4 & 16 & 8 \\ 2 & 16 & 8 & 4 & 4 & 1 & 16 & 8 \\ 8 & 4 & 2 & 4 & 16 & 16 & 1 & 8 \\ 4 & 8 & 4 & 2 & 8 & 8 & 8 & 1 \end{array}\right)\)

Isogeny graph