Elliptic curve isogeny class 21609.1-a over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-21609.1-a
• Conductor: 21609.1
• Rank: \( 0 \)

Base field \(\Q(\sqrt{-1}) \)

Generator \(i\), with minimal polynomial \( x^{2} + 1 \); class number \(1\).

Elliptic curves in class 21609.1-a over \(\Q(\sqrt{-1}) \)

Isogeny class 21609.1-a contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
21609.1-a1	\( \bigl[i\) , \( -1\) , \( i\) , \( -1666\) , \( -72764\bigr] \)
21609.1-a2	\( \bigl[i\) , \( -1\) , \( i\) , \( 49\) , \( -48\bigr] \)
21609.1-a3	\( \bigl[i\) , \( -1\) , \( i\) , \( -196\) , \( -146\bigr] \)
21609.1-a4	\( \bigl[i\) , \( -1\) , \( i\) , \( -1911\) , \( 32782\bigr] \)
21609.1-a5	\( \bigl[i\) , \( -1\) , \( i\) , \( -2401\) , \( -44246\bigr] \)
21609.1-a6	\( \bigl[i\) , \( -1\) , \( i\) , \( -38416\) , \( -2882228\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 8 & 2 & 4 \\ 8 & 1 & 2 & 4 & 4 & 8 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 4 & 2 & 1 & 4 & 8 \\ 2 & 4 & 2 & 4 & 1 & 2 \\ 4 & 8 & 4 & 8 & 2 & 1 \end{array}\right)\)

Isogeny graph