Properties

Base field \(\Q(\sqrt{-2}) \)
Label 2.0.8.1-9216.1-d
Conductor 9216.1
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 9216.1-d over \(\Q(\sqrt{-2}) \)

Isogeny class 9216.1-d contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
9216.1-d1 \( \bigl[0\) , \( 0\) , \( 0\) , \( -4 a + 2\) , \( 0\bigr] \)
9216.1-d2 \( \bigl[0\) , \( 0\) , \( 0\) , \( 4 a - 2\) , \( 0\bigr] \)
9216.1-d3 \( \bigl[0\) , \( 0\) , \( 0\) , \( 44 a - 22\) , \( -140 a - 56\bigr] \)
9216.1-d4 \( \bigl[0\) , \( 0\) , \( 0\) , \( 44 a - 22\) , \( 140 a + 56\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph