Properties

Base field \(\Q(\sqrt{-7}) \)
Label 2.0.7.1-28672.8-k
Conductor 28672.8
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 28672.8-k over \(\Q(\sqrt{-7}) \)

Isogeny class 28672.8-k contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
28672.8-k1 \( \bigl[0\) , \( -1\) , \( 0\) , \( a + 2\) , \( -a - 2\bigr] \)
28672.8-k2 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -2 a + 2\) , \( 0\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph