Elliptic curve isogeny class 896.2-a over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-896.2-a
• Conductor: 896.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 896.2-a over \(\Q(\sqrt{-7}) \)

Isogeny class 896.2-a contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
896.2-a1	\( \bigl[a\) , \( a + 1\) , \( a\) , \( 107 a - 128\) , \( -577 a + 141\bigr] \)
896.2-a2	\( \bigl[a\) , \( 0\) , \( a\) , \( -10 a + 29\) , \( 32 a + 18\bigr] \)
896.2-a3	\( \bigl[a\) , \( a + 1\) , \( a\) , \( 7 a - 8\) , \( -9 a - 3\bigr] \)
896.2-a4	\( \bigl[a\) , \( -a\) , \( 0\) , \( -2 a + 3\) , \( 5\bigr] \)
896.2-a5	\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 5 a + 20\) , \( 33 a - 15\bigr] \)
896.2-a6	\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -5 a\) , \( 5 a - 7\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph