Elliptic curve isogeny class 362.2-a over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-362.2-a
• Conductor: 362.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 362.2-a over \(\Q(\sqrt{-1}) \)

Isogeny class 362.2-a contains 3 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
362.2-a1	\( \bigl[1\) , \( -i - 1\) , \( 1\) , \( -i\) , \( 0\bigr] \)
362.2-a2	\( \bigl[1\) , \( -i - 1\) , \( 1\) , \( 9 i - 5\) , \( -2 i + 4\bigr] \)
362.2-a3	\( \bigl[1\) , \( -i - 1\) , \( 1\) , \( 449 i - 220\) , \( 4232 i + 646\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph