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

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

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

Curve label	Weierstrass Coefficients
525.1-e1	\( \bigl[a + 1\) , \( -a + 1\) , \( a\) , \( -509 a - 988\) , \( 12258 a + 22148\bigr] \)
525.1-e2	\( \bigl[a\) , \( 1\) , \( a + 1\) , \( -88 a + 244\) , \( -970 a + 2706\bigr] \)
525.1-e3	\( \bigl[a\) , \( 1\) , \( a + 1\) , \( 37 a - 106\) , \( -125 a + 346\bigr] \)
525.1-e4	\( \bigl[a\) , \( 1\) , \( a + 1\) , \( 12 a - 36\) , \( 42 a - 120\bigr] \)
525.1-e5	\( \bigl[a\) , \( 1\) , \( a + 1\) , \( 562 a - 1576\) , \( -10688 a + 29830\bigr] \)
525.1-e6	\( \bigl[a\) , \( 1\) , \( a + 1\) , \( 507 a - 1496\) , \( -12259 a + 34406\bigr] \)

Rank

Rank: \( 1 \)

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