Elliptic curve isogeny class 265.1-a over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-265.1-a
• Conductor: 265.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 265.1-a over \(\Q(\sqrt{-1}) \)

Isogeny class 265.1-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
265.1-a1	\( \bigl[i + 1\) , \( -i\) , \( i\) , \( -1\) , \( -i\bigr] \)
265.1-a2	\( \bigl[i + 1\) , \( i - 1\) , \( i\) , \( -i - 3\) , \( -2 i + 3\bigr] \)
265.1-a3	\( \bigl[i + 1\) , \( i - 1\) , \( i\) , \( -26 i + 22\) , \( 41 i + 69\bigr] \)
265.1-a4	\( \bigl[i + 1\) , \( -i\) , \( i\) , \( 95 i - 86\) , \( -520 i + 192\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph