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

• Base field: \(\Q(\sqrt{7}) \)
• Label: 2.2.28.1-567.1-c
• Conductor: 567.1
• Rank: \( 1 \)

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

Generator \(a\), with minimal polynomial \( x^{2} - 7 \); class number \(1\).

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

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

Curve label	Weierstrass Coefficients
567.1-c1	\( \bigl[a\) , \( -1\) , \( 0\) , \( -306\) , \( -5859\bigr] \)
567.1-c2	\( \bigl[a\) , \( -1\) , \( 0\) , \( 1035 a - 2871\) , \( -29241 a + 82944\bigr] \)
567.1-c3	\( \bigl[a\) , \( -1\) , \( 0\) , \( 9\) , \( 0\bigr] \)
567.1-c4	\( \bigl[a\) , \( -1\) , \( 0\) , \( -36\) , \( -27\bigr] \)
567.1-c5	\( \bigl[a\) , \( -1\) , \( 0\) , \( -351\) , \( 2430\bigr] \)
567.1-c6	\( \bigl[a\) , \( -1\) , \( 0\) , \( -441\) , \( -3672\bigr] \)
567.1-c7	\( \bigl[a\) , \( -1\) , \( 0\) , \( -1035 a - 2871\) , \( 29241 a + 82944\bigr] \)
567.1-c8	\( \bigl[a\) , \( -1\) , \( 0\) , \( -7056\) , \( -229905\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph