Properties

Base field \(\Q(\sqrt{-2}) \)
Label 2.0.8.1-7056.2-f
Conductor 7056.2
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 7056.2-f over \(\Q(\sqrt{-2}) \)

Isogeny class 7056.2-f contains 8 curves linked by isogenies of degrees dividing 16.

Curve label Weierstrass Coefficients
7056.2-f1 \( \bigl[a\) , \( 0\) , \( a\) , \( -15\) , \( 58\bigr] \)
7056.2-f2 \( \bigl[a\) , \( 0\) , \( a\) , \( 1545\) , \( 8674\bigr] \)
7056.2-f3 \( \bigl[a\) , \( 0\) , \( a\) , \( -415\) , \( 1226\bigr] \)
7056.2-f4 \( \bigl[a\) , \( 0\) , \( a\) , \( -3655\) , \( -83662\bigr] \)
7056.2-f5 \( \bigl[a\) , \( 0\) , \( a\) , \( -2380 a + 17225\) , \( 605612 a + 254850\bigr] \)
7056.2-f6 \( \bigl[a\) , \( 0\) , \( a\) , \( 2380 a + 17225\) , \( -605612 a + 254850\bigr] \)
7056.2-f7 \( \bigl[a\) , \( 0\) , \( a\) , \( -335\) , \( 2426\bigr] \)
7056.2-f8 \( \bigl[a\) , \( 0\) , \( a\) , \( -5375\) , \( 152618\bigr] \)

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