Properties

Base field \(\Q(\sqrt{-2}) \)
Label 2.0.8.1-26136.6-i
Conductor 26136.6
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 26136.6-i over \(\Q(\sqrt{-2}) \)

Isogeny class 26136.6-i contains 8 curves linked by isogenies of degrees dividing 16.

Curve label Weierstrass Coefficients
26136.6-i1 \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 78 a + 66\) , \( -2936 a - 46\bigr] \)
26136.6-i2 \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 14 a + 11\) , \( -43 a + 4\bigr] \)
26136.6-i3 \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -22 a - 19\) , \( 46 a - 16\bigr] \)
26136.6-i4 \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -122 a - 104\) , \( -724 a - 126\bigr] \)
26136.6-i5 \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 2868 a - 1374\) , \( -71480 a - 30430\bigr] \)
26136.6-i6 \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 488 a + 4226\) , \( -74840 a + 27698\bigr] \)
26136.6-i7 \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -322 a - 274\) , \( 3364 a - 136\bigr] \)
26136.6-i8 \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -1922 a - 1634\) , \( -48352 a - 3366\bigr] \)

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