Properties

Base field \(\Q(\sqrt{2}) \)
Label 2.2.8.1-56.2-a
Conductor 56.2
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 56.2-a over \(\Q(\sqrt{2}) \)

Isogeny class 56.2-a contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
56.2-a1 \( \bigl[a\) , \( a\) , \( a\) , \( -27\) , \( -21 a - 74\bigr] \)
56.2-a2 \( \bigl[a\) , \( a\) , \( a\) , \( 10 a - 7\) , \( -15 a + 20\bigr] \)
56.2-a3 \( \bigl[a\) , \( a\) , \( a\) , \( -2\) , \( -a - 1\bigr] \)
56.2-a4 \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -2 a - 1\) , \( a + 2\bigr] \)
56.2-a5 \( \bigl[a\) , \( a\) , \( a\) , \( -10 a - 17\) , \( -31 a - 44\bigr] \)
56.2-a6 \( \bigl[a\) , \( -a\) , \( 0\) , \( -105 a + 134\) , \( 86 a - 139\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph