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

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-7168.5-e
• Conductor: 7168.5
• Rank: \( 1 \)

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

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

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

Isogeny class 7168.5-e contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
7168.5-e1	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -2 a - 5\) , \( 3 a + 5\bigr] \)
7168.5-e2	\( \bigl[0\) , \( -1\) , \( 0\) , \( 5 a - 7\) , \( -5 a + 7\bigr] \)
7168.5-e3	\( \bigl[0\) , \( -1\) , \( 0\) , \( 45 a - 47\) , \( 131 a - 17\bigr] \)
7168.5-e4	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -11 a - 18\) , \( -48 a - 18\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph