Elliptic curve isogeny class 21.1-b over number field \(\Q(\sqrt{21}) \)

• Base field: \(\Q(\sqrt{21}) \)
• Label: 2.2.21.1-21.1-b
• Conductor: 21.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 21.1-b over \(\Q(\sqrt{21}) \)

Isogeny class 21.1-b contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
21.1-b1	\( \bigl[1\) , \( 0\) , \( 0\) , \( -34\) , \( -217\bigr] \)
21.1-b2	\( \bigl[1\) , \( 0\) , \( 0\) , \( 1\) , \( 0\bigr] \)
21.1-b3	\( \bigl[1\) , \( 0\) , \( 0\) , \( -4\) , \( -1\bigr] \)
21.1-b4	\( \bigl[1\) , \( 0\) , \( 0\) , \( -39\) , \( 90\bigr] \)
21.1-b5	\( \bigl[1\) , \( 0\) , \( 0\) , \( -49\) , \( -136\bigr] \)
21.1-b6	\( \bigl[1\) , \( 0\) , \( 0\) , \( -784\) , \( -8515\bigr] \)

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