Elliptic curve isogeny class 1183.1-e over number field \(\Q(\sqrt{21}) \)

• Base field: \(\Q(\sqrt{21}) \)
• Label: 2.2.21.1-1183.1-e
• Conductor: 1183.1
• Rank: \( 2 \)

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

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

Elliptic curves in class 1183.1-e over \(\Q(\sqrt{21}) \)

Isogeny class 1183.1-e contains 3 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
1183.1-e1	\( \bigl[0\) , \( 1\) , \( 1\) , \( -7\) , \( 5\bigr] \)
1183.1-e2	\( \bigl[0\) , \( 1\) , \( 1\) , \( -117\) , \( -1245\bigr] \)
1183.1-e3	\( \bigl[0\) , \( 1\) , \( 1\) , \( 13\) , \( 42\bigr] \)

Rank

Rank: \( 2 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)

Isogeny graph