Elliptic curve isogeny class 1083.1-a over number field \(\Q(\sqrt{21}) \)

• Base field: \(\Q(\sqrt{21}) \)
• Label: 2.2.21.1-1083.1-a
• Conductor: 1083.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 1083.1-a over \(\Q(\sqrt{21}) \)

Isogeny class 1083.1-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
1083.1-a1	\( \bigl[a\) , \( 1\) , \( a + 1\) , \( -43 a + 118\) , \( 659 a - 1842\bigr] \)
1083.1-a2	\( \bigl[a\) , \( 1\) , \( a + 1\) , \( 7 a - 22\) , \( -11 a + 28\bigr] \)
1083.1-a3	\( \bigl[a\) , \( 1\) , \( a + 1\) , \( 32 a - 92\) , \( 158 a - 444\bigr] \)
1083.1-a4	\( \bigl[a + 1\) , \( -a + 1\) , \( a\) , \( -509 a - 914\) , \( -9754 a - 17480\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph