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

• Base field: \(\Q(\sqrt{21}) \)
• Label: 2.2.21.1-525.1-c
• Conductor: 525.1
• Rank: \( 1 \)

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

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

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

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

Curve label	Weierstrass Coefficients
525.1-c1	\( \bigl[a\) , \( a + 1\) , \( 0\) , \( 125 a + 194\) , \( 3909 a + 7065\bigr] \)
525.1-c2	\( \bigl[1\) , \( 0\) , \( 0\) , \( -5 a + 14\) , \( 0\bigr] \)
525.1-c3	\( \bigl[1\) , \( 0\) , \( 0\) , \( 20 a - 56\) , \( 5 a - 14\bigr] \)
525.1-c4	\( \bigl[a\) , \( a + 1\) , \( 0\) , \( -100 a - 181\) , \( 594 a + 1065\bigr] \)
525.1-c5	\( \bigl[1\) , \( 0\) , \( 0\) , \( 225 a - 631\) , \( 2804 a - 7829\bigr] \)
525.1-c6	\( \bigl[1\) , \( 0\) , \( 0\) , \( 110 a - 321\) , \( -5045 a + 14101\bigr] \)

Rank

Rank: \( 1 \)

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