Elliptic curve isogeny class 896.7-a over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-896.7-a
• Conductor: 896.7
• Rank: \( 1 \)

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

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

Elliptic curves in class 896.7-a over \(\Q(\sqrt{-7}) \)

Isogeny class 896.7-a contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
896.7-a1	\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -107 a - 23\) , \( 555 a - 201\bigr] \)
896.7-a2	\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 8 a + 19\) , \( -33 a + 50\bigr] \)
896.7-a3	\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -7 a - 3\) , \( 7 a + 3\bigr] \)
896.7-a4	\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 2 a + 1\) , \( 5\bigr] \)
896.7-a5	\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -7 a + 25\) , \( -34 a + 18\bigr] \)
896.7-a6	\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 3 a - 5\) , \( -6 a - 2\bigr] \)

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