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

• Base field: \(\Q(\sqrt{21}) \)
• Label: 2.2.21.1-525.1-f
• 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-f over \(\Q(\sqrt{21}) \)

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

Curve label	Weierstrass Coefficients
525.1-f1	\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 153 a - 410\) , \( 1627 a - 4685\bigr] \)
525.1-f2	\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -2 a\) , \( -a\bigr] \)
525.1-f3	\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -2 a - 5\) , \( -3\bigr] \)
525.1-f4	\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 3 a - 35\) , \( 22 a - 110\bigr] \)
525.1-f5	\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -7 a - 55\) , \( 22 a + 112\bigr] \)
525.1-f6	\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -67 a - 140\) , \( -475 a - 1083\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph