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

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-7168.5-a
• 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-a over \(\Q(\sqrt{-7}) \)

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

Curve label	Weierstrass Coefficients
7168.5-a1	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -18 a - 5\) , \( -63 a + 35\bigr] \)
7168.5-a2	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 2 a\) , \( a\bigr] \)
7168.5-a3	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 2 a - 5\) , \( -3 a + 3\bigr] \)
7168.5-a4	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 22 a - 85\) , \( -119 a + 243\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph