Properties

Base field \(\Q(\sqrt{-7}) \)
Label 2.0.7.1-28672.9-a
Conductor 28672.9
Rank \( 1 \)

Related objects

Learn more

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

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

Elliptic curves in class 28672.9-a over \(\Q(\sqrt{-7}) \)

Isogeny class 28672.9-a contains 4 curves linked by isogenies of degrees dividing 10.

Curve label Weierstrass Coefficients
28672.9-a1 \( \bigl[0\) , \( a - 1\) , \( 0\) , \( 12 a - 64\) , \( -76 a + 204\bigr] \)
28672.9-a2 \( \bigl[0\) , \( a - 1\) , \( 0\) , \( 82 a + 76\) , \( 64 a - 860\bigr] \)
28672.9-a3 \( \bigl[0\) , \( a - 1\) , \( 0\) , \( 2 a - 4\) , \( 4\bigr] \)
28672.9-a4 \( \bigl[0\) , \( a - 1\) , \( 0\) , \( 92 a + 976\) , \( -9324 a + 6188\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph