Elliptic curve isogeny class 164.1-a over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-164.1-a
• Conductor: 164.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 164.1-a over \(\Q(\sqrt{-1}) \)

Isogeny class 164.1-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
164.1-a1	\( \bigl[i + 1\) , \( i + 1\) , \( i + 1\) , \( 5 i\) , \( 4 i + 1\bigr] \)
164.1-a2	\( \bigl[i + 1\) , \( i - 1\) , \( 0\) , \( -i\) , \( 0\bigr] \)
164.1-a3	\( \bigl[i + 1\) , \( i + 1\) , \( i + 1\) , \( -25 i - 10\) , \( 10 i + 15\bigr] \)
164.1-a4	\( \bigl[i + 1\) , \( i - 1\) , \( 0\) , \( -21 i - 10\) , \( -38 i + 18\bigr] \)

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