Elliptic curve isogeny class 567.1-a over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-567.1-a
• Conductor: 567.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 567.1-a over \(\Q(\sqrt{-7}) \)

Isogeny class 567.1-a contains 8 curves linked by isogenies of degrees dividing 16.

Curve label	Weierstrass Coefficients
567.1-a1	\( \bigl[1\) , \( -1\) , \( 0\) , \( -306\) , \( 5859\bigr] \)
567.1-a2	\( \bigl[1\) , \( -1\) , \( 0\) , \( 9\) , \( 0\bigr] \)
567.1-a3	\( \bigl[1\) , \( -1\) , \( 0\) , \( -36\) , \( 27\bigr] \)
567.1-a4	\( \bigl[1\) , \( -1\) , \( 0\) , \( -351\) , \( -2430\bigr] \)
567.1-a5	\( \bigl[1\) , \( -1\) , \( 0\) , \( 18 a - 3\) , \( 10 a + 36\bigr] \)
567.1-a6	\( \bigl[1\) , \( -1\) , \( 0\) , \( -18 a + 15\) , \( -10 a + 46\bigr] \)
567.1-a7	\( \bigl[1\) , \( -1\) , \( 0\) , \( -441\) , \( 3672\bigr] \)
567.1-a8	\( \bigl[1\) , \( -1\) , \( 0\) , \( -7056\) , \( 229905\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph