Elliptic curve isogeny class 128.5-a over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-128.5-a
• Conductor: 128.5
• Rank: \( 0 \)

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

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

Elliptic curves in class 128.5-a over \(\Q(\sqrt{-7}) \)

Isogeny class 128.5-a contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
128.5-a1	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 21 a - 22\) , \( 40 a - 16\bigr] \)
128.5-a2	\( \bigl[0\) , \( a\) , \( 0\) , \( -21 a - 1\) , \( 40 a - 24\bigr] \)
128.5-a3	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 2 a - 4\) , \( -a + 2\bigr] \)
128.5-a4	\( \bigl[0\) , \( -a\) , \( 0\) , \( -2 a - 2\) , \( -a - 1\bigr] \)
128.5-a5	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( a - 2\) , \( 0\bigr] \)
128.5-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