Properties

Base field \(\Q(\sqrt{-2}) \)
Label 2.0.8.1-6912.3-j
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-j over \(\Q(\sqrt{-2}) \)

Isogeny class 6912.3-j contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
6912.3-j1 \( \bigl[0\) , \( a - 1\) , \( 0\) , \( -32 a - 160\) , \( -272 a - 680\bigr] \)
6912.3-j2 \( \bigl[0\) , \( a - 1\) , \( 0\) , \( -96 a + 96\) , \( 148 a + 844\bigr] \)
6912.3-j3 \( \bigl[0\) , \( a - 1\) , \( 0\) , \( 28 a - 40\) , \( -140 a + 52\bigr] \)
6912.3-j4 \( \bigl[0\) , \( a - 1\) , \( 0\) , \( 4 a + 56\) , \( -104 a + 16\bigr] \)
6912.3-j5 \( \bigl[0\) , \( a - 1\) , \( 0\) , \( -6 a + 6\) , \( 4 a + 16\bigr] \)
6912.3-j6 \( \bigl[0\) , \( a - 1\) , \( 0\) , \( -2 a - 10\) , \( -8 a - 8\bigr] \)

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