Elliptic curve isogeny class 5330.8-a over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-5330.8-a
• Conductor: 5330.8
• Rank: \( 1 \)

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

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

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 6 & 2 & 3 \\ 6 & 1 & 3 & 2 \\ 2 & 3 & 1 & 6 \\ 3 & 2 & 6 & 1 \end{array}\right)\)

Isogeny graph

Elliptic curves in class 5330.8-a over \(\Q(\sqrt{-1}) \)

Isogeny class 5330.8-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
5330.8-a1	\( \bigl[1\) , \( 1\) , \( 0\) , \( 3 i - 19\) , \( -30 i + 162\bigr] \)
5330.8-a2	\( \bigl[i\) , \( -1\) , \( 0\) , \( -137 i + 16\) , \( 184 i - 435\bigr] \)
5330.8-a3	\( \bigl[i\) , \( -1\) , \( 0\) , \( 23 i + 11\) , \( -18 i - 52\bigr] \)
5330.8-a4	\( \bigl[1\) , \( 1\) , \( 0\) , \( -1977 i + 376\) , \( -17592 i + 30587\bigr] \)