Elliptic curve isogeny class 24336.3-a over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-24336.3-a
• Conductor: 24336.3
• Rank: \( 1 \)

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

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

Elliptic curves in class 24336.3-a over \(\Q(\sqrt{-1}) \)

Isogeny class 24336.3-a contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
24336.3-a1	\( \bigl[i + 1\) , \( i + 1\) , \( 0\) , \( -46 i - 20\) , \( -222 i - 988\bigr] \)
24336.3-a2	\( \bigl[0\) , \( -i\) , \( 0\) , \( 8 i + 3\) , \( -13 i + 5\bigr] \)
24336.3-a3	\( \bigl[i + 1\) , \( i + 1\) , \( 0\) , \( 14 i + 5\) , \( 10 i + 10\bigr] \)
24336.3-a4	\( \bigl[i + 1\) , \( i + 1\) , \( 0\) , \( 74 i + 30\) , \( -10 i - 280\bigr] \)
24336.3-a5	\( \bigl[i + 1\) , \( i + 1\) , \( 0\) , \( 194 i + 80\) , \( 328 i + 1072\bigr] \)
24336.3-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