Elliptic curve isogeny class 7168.7-g over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-7168.7-g
• Conductor: 7168.7
• Rank: \( 1 \)

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

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

Elliptic curves in class 7168.7-g over \(\Q(\sqrt{-7}) \)

Isogeny class 7168.7-g contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
7168.7-g1	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 0\) , \( -4 a + 12\bigr] \)
7168.7-g2	\( \bigl[0\) , \( a\) , \( 0\) , \( 14 a - 3\) , \( 13 a + 14\bigr] \)
7168.7-g3	\( \bigl[0\) , \( -a\) , \( 0\) , \( 2 a + 17\) , \( -29 a + 18\bigr] \)
7168.7-g4	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 40 a + 40\) , \( -84 a + 252\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph