Properties

Base field \(\Q(\sqrt{-7}) \)
Label 2.0.7.1-128.4-a
Conductor 128.4
Rank \( 0 \)

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

Isogeny class 128.4-a contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
128.4-a1 \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 21 a - 22\) , \( -40 a + 16\bigr] \)
128.4-a2 \( \bigl[0\) , \( -a\) , \( 0\) , \( -21 a - 1\) , \( -40 a + 24\bigr] \)
128.4-a3 \( \bigl[0\) , \( a - 1\) , \( 0\) , \( 2 a - 4\) , \( a - 2\bigr] \)
128.4-a4 \( \bigl[0\) , \( a\) , \( 0\) , \( -2 a - 2\) , \( a + 1\bigr] \)
128.4-a5 \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( a - 2\) , \( 0\bigr] \)
128.4-a6 \( \bigl[0\) , \( -a\) , \( 0\) , \( -a - 1\) , \( 0\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph