Elliptic curve isogeny class 1089.1-e over number field \(\Q(\sqrt{21}) \)

• Base field: \(\Q(\sqrt{21}) \)
• Label: 2.2.21.1-1089.1-e
• Conductor: 1089.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 1089.1-e over \(\Q(\sqrt{21}) \)

Isogeny class 1089.1-e contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
1089.1-e1	\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( 7 a - 21\) , \( 6 a - 17\bigr] \)
1089.1-e2	\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( -83 a - 149\) , \( -726 a - 1301\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph