Properties

Base field \(\Q(\sqrt{-2}) \)
Label 2.0.8.1-7938.3-a
Conductor 7938.3
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 7938.3-a over \(\Q(\sqrt{-2}) \)

Isogeny class 7938.3-a contains 8 curves linked by isogenies of degrees dividing 16.

Curve label Weierstrass Coefficients
7938.3-a1 \( \bigl[1\) , \( -1\) , \( 0\) , \( -36\) , \( -176\bigr] \)
7938.3-a2 \( \bigl[1\) , \( -1\) , \( 0\) , \( 3474\) , \( -31010\bigr] \)
7938.3-a3 \( \bigl[1\) , \( -1\) , \( 0\) , \( -936\) , \( -3668\bigr] \)
7938.3-a4 \( \bigl[1\) , \( -1\) , \( 0\) , \( -8226\) , \( 286474\bigr] \)
7938.3-a5 \( \bigl[1\) , \( -1\) , \( 0\) , \( -5355 a + 38754\) , \( -2041263 a - 879494\bigr] \)
7938.3-a6 \( \bigl[1\) , \( -1\) , \( 0\) , \( 5355 a + 38754\) , \( 2041263 a - 879494\bigr] \)
7938.3-a7 \( \bigl[1\) , \( -1\) , \( 0\) , \( -756\) , \( -7808\bigr] \)
7938.3-a8 \( \bigl[1\) , \( -1\) , \( 0\) , \( -12096\) , \( -509036\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph