Properties

Base field \(\Q(\sqrt{-7}) \)
Label 2.0.7.1-28672.5-a
Conductor 28672.5
Rank \( 1 \)

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 28672.5-a over \(\Q(\sqrt{-7}) \)

Isogeny class 28672.5-a contains 4 curves linked by isogenies of degrees dividing 10.

Curve label Weierstrass Coefficients
28672.5-a1 \( \bigl[0\) , \( -a\) , \( 0\) , \( -12 a - 52\) , \( 76 a + 128\bigr] \)
28672.5-a2 \( \bigl[0\) , \( -a\) , \( 0\) , \( -92 a + 1068\) , \( 9324 a - 3136\bigr] \)
28672.5-a3 \( \bigl[0\) , \( -a\) , \( 0\) , \( -2 a - 2\) , \( 4\bigr] \)
28672.5-a4 \( \bigl[0\) , \( -a\) , \( 0\) , \( -82 a + 158\) , \( -64 a - 796\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 5 & 2 & 10 \\ 5 & 1 & 10 & 2 \\ 2 & 10 & 1 & 5 \\ 10 & 2 & 5 & 1 \end{array}\right)\)

Isogeny graph