Properties

Base field \(\Q(\sqrt{-2}) \)
Label 2.0.8.1-6912.2-m
Conductor 6912.2
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 6912.2-m over \(\Q(\sqrt{-2}) \)

Isogeny class 6912.2-m contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
6912.2-m1 \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 96 a + 96\) , \( -148 a + 844\bigr] \)
6912.2-m2 \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 32 a - 160\) , \( 272 a - 680\bigr] \)
6912.2-m3 \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -4 a + 56\) , \( 104 a + 16\bigr] \)
6912.2-m4 \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -28 a - 40\) , \( 140 a + 52\bigr] \)
6912.2-m5 \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 2 a - 10\) , \( 8 a - 8\bigr] \)
6912.2-m6 \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 6 a + 6\) , \( -4 a + 16\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph