Properties

Base field \(\Q(\sqrt{-2}) \)
Label 2.0.8.1-72.2-a
Conductor 72.2
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 72.2-a over \(\Q(\sqrt{-2}) \)

Isogeny class 72.2-a contains 8 curves linked by isogenies of degrees dividing 16.

Curve label Weierstrass Coefficients
72.2-a1 \( \bigl[a\) , \( 1\) , \( a\) , \( 5\) , \( 23\bigr] \)
72.2-a2 \( \bigl[0\) , \( -1\) , \( 0\) , \( 1\) , \( 0\bigr] \)
72.2-a3 \( \bigl[a\) , \( 1\) , \( a\) , \( 0\) , \( 0\bigr] \)
72.2-a4 \( \bigl[a\) , \( 1\) , \( a\) , \( -5\) , \( 5\bigr] \)
72.2-a5 \( \bigl[a\) , \( 1\) , \( a\) , \( 70 a + 85\) , \( -98 a + 559\bigr] \)
72.2-a6 \( \bigl[a\) , \( 1\) , \( a\) , \( -70 a + 85\) , \( 98 a + 559\bigr] \)
72.2-a7 \( \bigl[a\) , \( 1\) , \( a\) , \( -15\) , \( -27\bigr] \)
72.2-a8 \( \bigl[a\) , \( 1\) , \( a\) , \( -95\) , \( 347\bigr] \)

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