Properties

Base field \(\Q(\sqrt{-2}) \)
Label 2.0.8.1-46818.8-k
Conductor 46818.8
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 46818.8-k over \(\Q(\sqrt{-2}) \)

Isogeny class 46818.8-k contains 8 curves linked by isogenies of degrees dividing 16.

Curve label Weierstrass Coefficients
46818.8-k1 \( \bigl[1\) , \( -1\) , \( 0\) , \( -14796\) , \( 835434\bigr] \)
46818.8-k2 \( \bigl[1\) , \( -1\) , \( 0\) , \( 38745 a - 8316\) , \( 3718953 a + 3437478\bigr] \)
46818.8-k3 \( \bigl[1\) , \( -1\) , \( 0\) , \( -38745 a - 8316\) , \( -3718953 a + 3437478\bigr] \)
46818.8-k4 \( \bigl[1\) , \( -1\) , \( 0\) , \( 2034\) , \( 60264\bigr] \)
46818.8-k5 \( \bigl[1\) , \( -1\) , \( 0\) , \( -1026\) , \( 10692\bigr] \)
46818.8-k6 \( \bigl[1\) , \( -1\) , \( 0\) , \( -306\) , \( -1836\bigr] \)
46818.8-k7 \( \bigl[1\) , \( -1\) , \( 0\) , \( -15606\) , \( 754272\bigr] \)
46818.8-k8 \( \bigl[1\) , \( -1\) , \( 0\) , \( -249696\) , \( 48087270\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph