Elliptic curve isogeny class 2592.2-a over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-2592.2-a
• Conductor: 2592.2
• Rank: \( 0 \)

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

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

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 4 & 4 & 2 & 2 & 2 & 4 & 4 \\ 4 & 1 & 16 & 8 & 8 & 2 & 16 & 4 \\ 4 & 16 & 1 & 8 & 2 & 8 & 4 & 16 \\ 2 & 8 & 8 & 1 & 4 & 4 & 8 & 8 \\ 2 & 8 & 2 & 4 & 1 & 4 & 2 & 8 \\ 2 & 2 & 8 & 4 & 4 & 1 & 8 & 2 \\ 4 & 16 & 4 & 8 & 2 & 8 & 1 & 16 \\ 4 & 4 & 16 & 8 & 8 & 2 & 16 & 1 \end{array}\right)\)

Isogeny graph

Elliptic curves in class 2592.2-a over \(\Q(\sqrt{-7}) \)

Isogeny class 2592.2-a contains 8 curves linked by isogenies of degrees dividing 16.

Curve label	Weierstrass Coefficients
2592.2-a1	\( \bigl[a\) , \( -a - 1\) , \( a\) , \( 10 a - 5\) , \( -165 a + 397\bigr] \)
2592.2-a2	\( \bigl[a\) , \( -a - 1\) , \( a\) , \( -26 a - 77\) , \( 69 a + 177\bigr] \)
2592.2-a3	\( \bigl[a\) , \( -a - 1\) , \( a\) , \( -8 a + 103\) , \( -147 a + 33\bigr] \)
2592.2-a4	\( \bigl[a\) , \( -a - 1\) , \( a\) , \( -530 a + 355\) , \( -2685 a + 6877\bigr] \)
2592.2-a5	\( \bigl[a\) , \( -a - 1\) , \( a\) , \( 145 a + 1\) , \( 91 a + 1053\bigr] \)
2592.2-a6	\( \bigl[a\) , \( -a - 1\) , \( a\) , \( 127 a - 179\) , \( -883 a + 721\bigr] \)
2592.2-a7	\( \bigl[a\) , \( -a - 1\) , \( a\) , \( 2305 a + 1\) , \( 11323 a + 64125\bigr] \)
2592.2-a8	\( \bigl[a\) , \( -a - 1\) , \( a\) , \( 2017 a - 2879\) , \( -54451 a + 38737\bigr] \)