Properties

Base field \(\Q(\sqrt{-7}) \)
Label 2.0.7.1-28672.7-r
Conductor 28672.7
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 28672.7-r over \(\Q(\sqrt{-7}) \)

Isogeny class 28672.7-r contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
28672.7-r1 \( \bigl[0\) , \( 1\) , \( 0\) , \( 7 a + 2\) , \( -7 a - 4\bigr] \)
28672.7-r2 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 9 a - 15\) , \( -13 a - 1\bigr] \)
28672.7-r3 \( \bigl[0\) , \( -1\) , \( 0\) , \( 16 a - 1\) , \( -16 a - 31\bigr] \)
28672.7-r4 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 129 a - 215\) , \( -933 a + 711\bigr] \)

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