Elliptic curve isogeny class 88.2-a over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-88.2-a
• Conductor: 88.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 88.2-a over \(\Q(\sqrt{-7}) \)

Isogeny class 88.2-a contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
88.2-a1	\( \bigl[a\) , \( a\) , \( a\) , \( -6 a + 10\) , \( -a - 7\bigr] \)
88.2-a2	\( \bigl[a\) , \( a\) , \( a\) , \( -a\) , \( -a + 1\bigr] \)
88.2-a3	\( \bigl[a\) , \( a\) , \( a\) , \( -a + 20\) , \( 33 a - 35\bigr] \)
88.2-a4	\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 1\) , \( 0\bigr] \)
88.2-a5	\( \bigl[a\) , \( -1\) , \( a\) , \( -3 a + 6\) , \( -4\bigr] \)
88.2-a6	\( \bigl[a\) , \( a\) , \( a\) , \( -91 a + 160\) , \( -175 a - 611\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph