Elliptic curve isogeny class 289.1-a over number field \(\Q(\sqrt{21}) \)

• Base field: \(\Q(\sqrt{21}) \)
• Label: 2.2.21.1-289.1-a
• Conductor: 289.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 289.1-a over \(\Q(\sqrt{21}) \)

Isogeny class 289.1-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
289.1-a1	\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( 2 a - 7\) , \( -330 a + 921\bigr] \)
289.1-a2	\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( -3 a - 5\) , \( -6 a - 11\bigr] \)
289.1-a3	\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( 27 a - 77\) , \( -90 a + 251\bigr] \)
289.1-a4	\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( 452 a - 1267\) , \( -7434 a + 20753\bigr] \)

Rank

Rank: \( 0 \)

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