Properties

Base field \(\Q(\sqrt{-2}) \)
Label 2.0.8.1-6912.3-n
Conductor 6912.3
Rank \( 0 \)

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-n over \(\Q(\sqrt{-2}) \)

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

Curve label Weierstrass Coefficients
6912.3-n1 \( \bigl[0\) , \( a - 1\) , \( 0\) , \( -32 a - 16\) , \( 180 a + 900\bigr] \)
6912.3-n2 \( \bigl[0\) , \( a - 1\) , \( 0\) , \( -2 a - 1\) , \( 0\bigr] \)
6912.3-n3 \( \bigl[0\) , \( a - 1\) , \( 0\) , \( 8 a + 4\) , \( -4 a - 20\bigr] \)
6912.3-n4 \( \bigl[0\) , \( a - 1\) , \( 0\) , \( 48 a + 24\) , \( 36 a + 180\bigr] \)
6912.3-n5 \( \bigl[0\) , \( a - 1\) , \( 0\) , \( -952 a + 784\) , \( 548 a + 23908\bigr] \)
6912.3-n6 \( \bigl[0\) , \( a - 1\) , \( 0\) , \( -392 a - 1456\) , \( 8388 a + 20772\bigr] \)
6912.3-n7 \( \bigl[0\) , \( a - 1\) , \( 0\) , \( 128 a + 64\) , \( -220 a - 1100\bigr] \)
6912.3-n8 \( \bigl[0\) , \( a - 1\) , \( 0\) , \( 768 a + 384\) , \( 2772 a + 13860\bigr] \)

Rank

Rank: \( 0 \)

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