Properties

Base field \(\Q(\sqrt{-2}) \)
Label 2.0.8.1-7200.2-q
Conductor 7200.2
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 7200.2-q over \(\Q(\sqrt{-2}) \)

Isogeny class 7200.2-q contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
7200.2-q1 \( \bigl[a\) , \( 0\) , \( 0\) , \( 6\) , \( 495\bigr] \)
7200.2-q2 \( \bigl[a\) , \( 0\) , \( a\) , \( -123\) , \( -275\bigr] \)
7200.2-q3 \( \bigl[0\) , \( 1\) , \( 0\) , \( -226\) , \( -1360\bigr] \)
7200.2-q4 \( \bigl[a\) , \( 0\) , \( 0\) , \( 575 a + 506\) , \( -510 a + 11145\bigr] \)
7200.2-q5 \( \bigl[a\) , \( 0\) , \( 0\) , \( -575 a + 506\) , \( 510 a + 11145\bigr] \)
7200.2-q6 \( \bigl[0\) , \( 1\) , \( 0\) , \( -900\) , \( 10098\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph