Properties

Base field \(\Q(\sqrt{-7}) \)
Label 2.0.7.1-576.4-a
Conductor 576.4
Rank \( 0 \)

Related objects

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Base field \(\Q(\sqrt{-7}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x + 2 \); class number \(1\).

Elliptic curves in class 576.4-a over \(\Q(\sqrt{-7}) \)

Isogeny class 576.4-a contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
576.4-a1 \( \bigl[0\) , \( -1\) , \( 0\) , \( 16\) , \( -180\bigr] \)
576.4-a2 \( \bigl[0\) , \( -1\) , \( 0\) , \( 1\) , \( 0\bigr] \)
576.4-a3 \( \bigl[0\) , \( -1\) , \( 0\) , \( -4\) , \( 4\bigr] \)
576.4-a4 \( \bigl[0\) , \( -1\) , \( 0\) , \( -24\) , \( -36\bigr] \)
576.4-a5 \( \bigl[0\) , \( -1\) , \( 0\) , \( -64\) , \( 220\bigr] \)
576.4-a6 \( \bigl[0\) , \( -1\) , \( 0\) , \( -384\) , \( -2772\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph