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

• Base field: \(\Q(\sqrt{21}) \)
• Label: 2.2.21.1-21.1-a
• Conductor: 21.1
• Rank: \( 0 \)

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

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

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

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

Curve label	Weierstrass Coefficients
21.1-a1	\( \bigl[a\) , \( 1\) , \( a\) , \( 170 a - 477\) , \( -5038 a + 14062\bigr] \)
21.1-a2	\( \bigl[a\) , \( 1\) , \( a\) , \( -5 a + 13\) , \( -5 a + 13\bigr] \)
21.1-a3	\( \bigl[a\) , \( 1\) , \( a\) , \( 20 a - 57\) , \( -4 a + 10\bigr] \)
21.1-a4	\( \bigl[a\) , \( 1\) , \( a\) , \( 195 a - 547\) , \( 2355 a - 6577\bigr] \)
21.1-a5	\( \bigl[a\) , \( 1\) , \( a\) , \( 245 a - 687\) , \( -3019 a + 8425\bigr] \)
21.1-a6	\( \bigl[a\) , \( 1\) , \( a\) , \( 3920 a - 10977\) , \( -200440 a + 559528\bigr] \)

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