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

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-896.2-b
• Conductor: 896.2
• Rank: \( 0 \)

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

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

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

Isogeny class 896.2-b contains 12 curves linked by isogenies of degrees dividing 36.

Curve label	Weierstrass Coefficients
896.2-b1	\( \bigl[a\) , \( 1\) , \( a\) , \( -853 a - 340\) , \( -14854 a + 5243\bigr] \)
896.2-b2	\( \bigl[a\) , \( -1\) , \( a\) , \( 10 a + 134\) , \( -464 a + 263\bigr] \)
896.2-b3	\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 100 a - 88\) , \( -488 a - 48\bigr] \)
896.2-b4	\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 5 a + 2\) , \( -a + 6\bigr] \)
896.2-b5	\( \bigl[a\) , \( -1\) , \( a\) , \( 5 a + 4\) , \( -2 a - 13\bigr] \)
896.2-b6	\( \bigl[a\) , \( 1\) , \( a\) , \( -3 a\) , \( 4 a - 1\bigr] \)
896.2-b7	\( \bigl[a\) , \( 1\) , \( a\) , \( 22 a + 10\) , \( -98 a + 35\bigr] \)
896.2-b8	\( \bigl[a\) , \( -1\) , \( a\) , \( 15 a - 376\) , \( -2580 a + 1951\bigr] \)
896.2-b9	\( \bigl[a\) , \( a - 1\) , \( 0\) , \( -255 a + 282\) , \( -2259 a + 50\bigr] \)
896.2-b10	\( \bigl[a\) , \( 1\) , \( a\) , \( -178 a - 70\) , \( -1186 a + 419\bigr] \)
896.2-b11	\( \bigl[a\) , \( 1\) , \( a\) , \( -53 a - 20\) , \( 208 a - 73\bigr] \)
896.2-b12	\( \bigl[a\) , \( 1\) , \( a\) , \( -13653 a - 5460\) , \( -937478 a + 330875\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrrrrrr} 1 & 6 & 6 & 18 & 18 & 9 & 3 & 2 & 2 & 6 & 18 & 2 \\ 6 & 1 & 4 & 12 & 3 & 6 & 2 & 3 & 12 & 4 & 12 & 12 \\ 6 & 4 & 1 & 3 & 12 & 6 & 2 & 12 & 3 & 4 & 12 & 12 \\ 18 & 12 & 3 & 1 & 4 & 2 & 6 & 36 & 9 & 12 & 4 & 36 \\ 18 & 3 & 12 & 4 & 1 & 2 & 6 & 9 & 36 & 12 & 4 & 36 \\ 9 & 6 & 6 & 2 & 2 & 1 & 3 & 18 & 18 & 6 & 2 & 18 \\ 3 & 2 & 2 & 6 & 6 & 3 & 1 & 6 & 6 & 2 & 6 & 6 \\ 2 & 3 & 12 & 36 & 9 & 18 & 6 & 1 & 4 & 12 & 36 & 4 \\ 2 & 12 & 3 & 9 & 36 & 18 & 6 & 4 & 1 & 12 & 36 & 4 \\ 6 & 4 & 4 & 12 & 12 & 6 & 2 & 12 & 12 & 1 & 3 & 3 \\ 18 & 12 & 12 & 4 & 4 & 2 & 6 & 36 & 36 & 3 & 1 & 9 \\ 2 & 12 & 12 & 36 & 36 & 18 & 6 & 4 & 4 & 3 & 9 & 1 \end{array}\right)\)

Isogeny graph