Elliptic curve isogeny class 7168.5-b over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-7168.5-b
• Conductor: 7168.5
• Rank: \( 0 \)

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

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

Elliptic curves in class 7168.5-b over \(\Q(\sqrt{-7}) \)

Isogeny class 7168.5-b contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
7168.5-b1	\( \bigl[0\) , \( 1\) , \( 0\) , \( -171 a - 511\) , \( 2369 a + 3929\bigr] \)
7168.5-b2	\( \bigl[0\) , \( -1\) , \( 0\) , \( 65 a + 29\) , \( 23 a - 445\bigr] \)
7168.5-b3	\( \bigl[0\) , \( 1\) , \( 0\) , \( -11 a - 31\) , \( 33 a + 57\bigr] \)
7168.5-b4	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 6 a + 11\) , \( 41 a - 45\bigr] \)
7168.5-b5	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 70 a - 53\) , \( -213 a - 171\bigr] \)
7168.5-b6	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -10 a + 27\) , \( -37 a - 27\bigr] \)

Rank

Rank: \( 0 \)

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