Elliptic curve isogeny class 1452.1-a over number field \(\Q(\sqrt{21}) \)

• Base field: \(\Q(\sqrt{21}) \)
• Label: 2.2.21.1-1452.1-a
• Conductor: 1452.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 1452.1-a over \(\Q(\sqrt{21}) \)

Isogeny class 1452.1-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
1452.1-a1	\( \bigl[1\) , \( 1\) , \( 1\) , \( -12\) , \( -81\bigr] \)
1452.1-a2	\( \bigl[1\) , \( 1\) , \( 1\) , \( -2\) , \( -1\bigr] \)
1452.1-a3	\( \bigl[1\) , \( 1\) , \( 1\) , \( -22\) , \( -49\bigr] \)
1452.1-a4	\( \bigl[1\) , \( 1\) , \( 1\) , \( -352\) , \( -2689\bigr] \)

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