Elliptic curve isogeny class 567.2-b over number field \(\Q(\sqrt{29}) \)

• Base field: \(\Q(\sqrt{29}) \)
• Label: 2.2.29.1-567.2-b
• Conductor: 567.2
• Rank: \( 0 \)

Base field \(\Q(\sqrt{29}) \)

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

Elliptic curves in class 567.2-b over \(\Q(\sqrt{29}) \)

Isogeny class 567.2-b contains 4 curves linked by isogenies of degrees dividing 10.

Curve label	Weierstrass Coefficients
567.2-b1	\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -8 a - 266\) , \( 673 a + 23\bigr] \)
567.2-b2	\( \bigl[a\) , \( -a - 1\) , \( a\) , \( 34 a - 113\) , \( 8 a - 57\bigr] \)
567.2-b3	\( \bigl[a\) , \( -a - 1\) , \( a\) , \( -11 a + 22\) , \( -10 a + 24\bigr] \)
567.2-b4	\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -53 a - 131\) , \( 385 a + 824\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 5 & 10 & 2 \\ 5 & 1 & 2 & 10 \\ 10 & 2 & 1 & 5 \\ 2 & 10 & 5 & 1 \end{array}\right)\)

Isogeny graph