Elliptic curve isogeny class 164.2-a over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-164.2-a
• Conductor: 164.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 164.2-a over \(\Q(\sqrt{-1}) \)

Isogeny class 164.2-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
164.2-a1	\( \bigl[i + 1\) , \( i + 1\) , \( 0\) , \( -4 i\) , \( -4 i + 6\bigr] \)
164.2-a2	\( \bigl[i + 1\) , \( i - 1\) , \( i + 1\) , \( -2 i\) , \( 0\bigr] \)
164.2-a3	\( \bigl[i + 1\) , \( i + 1\) , \( 0\) , \( 26 i - 10\) , \( -20 i - 10\bigr] \)
164.2-a4	\( \bigl[i + 1\) , \( i - 1\) , \( i + 1\) , \( 18 i - 10\) , \( 28 i - 2\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph