Elliptic curve isogeny class 24336.1-a over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-24336.1-a
• Conductor: 24336.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 24336.1-a over \(\Q(\sqrt{-1}) \)

Isogeny class 24336.1-a contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
24336.1-a1	\( \bigl[i + 1\) , \( i - 1\) , \( 0\) , \( 46 i - 20\) , \( -222 i + 988\bigr] \)
24336.1-a2	\( \bigl[0\) , \( -i\) , \( 0\) , \( -8 i + 3\) , \( -13 i - 5\bigr] \)
24336.1-a3	\( \bigl[i + 1\) , \( i - 1\) , \( 0\) , \( -14 i + 5\) , \( 10 i - 10\bigr] \)
24336.1-a4	\( \bigl[i + 1\) , \( i - 1\) , \( 0\) , \( -74 i + 30\) , \( -10 i + 280\bigr] \)
24336.1-a5	\( \bigl[i + 1\) , \( i + 1\) , \( i + 1\) , \( -193 i + 80\) , \( -248 i + 1265\bigr] \)
24336.1-a6	\( \bigl[i + 1\) , \( i - 1\) , \( 0\) , \( -1154 i + 480\) , \( -2638 i + 17092\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 8 & 4 \\ 8 & 1 & 2 & 4 & 4 & 8 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 2 & 4 & 2 & 1 & 4 & 2 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 8 & 4 & 2 & 8 & 1 \end{array}\right)\)

Isogeny graph