Elliptic curve isogeny class 8320.4-a over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-8320.4-a
• Conductor: 8320.4
• Rank: \( 1 \)

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

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

Elliptic curves in class 8320.4-a over \(\Q(\sqrt{-1}) \)

Isogeny class 8320.4-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
8320.4-a1	\( \bigl[i + 1\) , \( -i - 1\) , \( i + 1\) , \( -i\) , \( -3 i + 6\bigr] \)
8320.4-a2	\( \bigl[0\) , \( -i - 1\) , \( 0\) , \( -8 i - 9\) , \( 21 i + 7\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph