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

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

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

Curve label	Weierstrass Coefficients
7168.5-d1	\( \bigl[0\) , \( 0\) , \( 0\) , \( a - 2\) , \( -2 a - 4\bigr] \)
7168.5-d2	\( \bigl[0\) , \( 0\) , \( 0\) , \( -59 a + 118\) , \( 138 a + 276\bigr] \)
7168.5-d3	\( \bigl[0\) , \( 0\) , \( 0\) , \( -19 a + 38\) , \( -30 a - 60\bigr] \)
7168.5-d4	\( \bigl[0\) , \( 0\) , \( 0\) , \( 10 a - 8\) , \( -13 a - 2\bigr] \)
7168.5-d5	\( \bigl[0\) , \( 0\) , \( 0\) , \( a - 14\) , \( 2 a - 20\bigr] \)
7168.5-d6	\( \bigl[0\) , \( 0\) , \( 0\) , \( -299 a + 598\) , \( -1990 a - 3980\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 4 & 2 & 2 & 2 & 4 \\ 4 & 1 & 2 & 8 & 8 & 4 \\ 2 & 2 & 1 & 4 & 4 & 2 \\ 2 & 8 & 4 & 1 & 4 & 8 \\ 2 & 8 & 4 & 4 & 1 & 8 \\ 4 & 4 & 2 & 8 & 8 & 1 \end{array}\right)\)

Isogeny graph