Elliptic curve isogeny class 525.1-k over number field \(\Q(\sqrt{21}) \)

• Base field: \(\Q(\sqrt{21}) \)
• Label: 2.2.21.1-525.1-k
• Conductor: 525.1
• Rank: \( 0 \)

Base field \(\Q(\sqrt{21}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 5 \); class number \(1\).

Elliptic curves in class 525.1-k over \(\Q(\sqrt{21}) \)

Isogeny class 525.1-k contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
525.1-k1	\( \bigl[1\) , \( 0\) , \( 1\) , \( 370 a - 1138\) , \( 6332 a - 18209\bigr] \)
525.1-k2	\( \bigl[1\) , \( 0\) , \( 1\) , \( 17\) , \( -37\bigr] \)
525.1-k3	\( \bigl[1\) , \( 0\) , \( 1\) , \( -8\) , \( -7\bigr] \)
525.1-k4	\( \bigl[1\) , \( 0\) , \( 1\) , \( -3\) , \( 1\bigr] \)
525.1-k5	\( \bigl[1\) , \( 0\) , \( 1\) , \( -113\) , \( -469\bigr] \)
525.1-k6	\( \bigl[1\) , \( 0\) , \( 1\) , \( -370 a - 768\) , \( -6332 a - 11877\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph