Elliptic curve isogeny class 84.1-a over number field \(\Q(\sqrt{21}) \)

• Base field: \(\Q(\sqrt{21}) \)
• Label: 2.2.21.1-84.1-a
• Conductor: 84.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 84.1-a over \(\Q(\sqrt{21}) \)

Isogeny class 84.1-a contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
84.1-a1	\( \bigl[a\) , \( a + 1\) , \( 1\) , \( 22 a - 52\) , \( 166 a - 457\bigr] \)
84.1-a2	\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 1930 a + 3476\) , \( -23318 a - 41795\bigr] \)
84.1-a3	\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -520 a - 934\) , \( -4404 a - 7887\bigr] \)
84.1-a4	\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -4570 a - 8224\) , \( 244590 a + 438261\bigr] \)
84.1-a5	\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -420 a - 754\) , \( -7864 a - 14087\bigr] \)
84.1-a6	\( \bigl[a\) , \( a + 1\) , \( 1\) , \( 6722 a - 18812\) , \( 455166 a - 1270777\bigr] \)

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