Elliptic curve isogeny class 28322.1-a over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-28322.1-a
• Conductor: 28322.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 28322.1-a over \(\Q(\sqrt{-1}) \)

Isogeny class 28322.1-a contains 6 curves linked by isogenies of degrees dividing 18.

Curve label	Weierstrass Coefficients
28322.1-a1	\( \bigl[1\) , \( -i\) , \( 1\) , \( 1364 i + 2557\) , \( -45435 i + 41066\bigr] \)
28322.1-a2	\( \bigl[1\) , \( -i\) , \( 1\) , \( 4 i + 7\) , \( 13 i - 12\bigr] \)
28322.1-a3	\( \bigl[1\) , \( -i\) , \( 1\) , \( -36 i - 68\) , \( -299 i + 270\bigr] \)
28322.1-a4	\( \bigl[1\) , \( -i\) , \( 1\) , \( 284 i + 532\) , \( -3627 i + 3278\bigr] \)
28322.1-a5	\( \bigl[1\) , \( -i\) , \( 1\) , \( 84 i + 157\) , \( 637 i - 576\bigr] \)
28322.1-a6	\( \bigl[1\) , \( -i\) , \( 1\) , \( 21844 i + 40957\) , \( -2867579 i + 2591850\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 9 & 3 & 6 & 18 & 2 \\ 9 & 1 & 3 & 6 & 2 & 18 \\ 3 & 3 & 1 & 2 & 6 & 6 \\ 6 & 6 & 2 & 1 & 3 & 3 \\ 18 & 2 & 6 & 3 & 1 & 9 \\ 2 & 18 & 6 & 3 & 9 & 1 \end{array}\right)\)

Isogeny graph