Elliptic curve isogeny class 24200.2-c over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-24200.2-c
• Conductor: 24200.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 24200.2-c over \(\Q(\sqrt{-1}) \)

Isogeny class 24200.2-c contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
24200.2-c1	\( \bigl[i + 1\) , \( i\) , \( 0\) , \( 656\) , \( 34034 i\bigr] \)
24200.2-c2	\( \bigl[i + 1\) , \( i\) , \( 0\) , \( 1886\) , \( -680 i\bigr] \)
24200.2-c3	\( \bigl[i + 1\) , \( i\) , \( 0\) , \( 12870 i - 4184\) , \( 560142 i + 195844\bigr] \)
24200.2-c4	\( \bigl[i + 1\) , \( i\) , \( 0\) , \( -12870 i - 4184\) , \( 560142 i - 195844\bigr] \)
24200.2-c5	\( \bigl[i + 1\) , \( i\) , \( 0\) , \( 1261\) , \( 17820 i\bigr] \)
24200.2-c6	\( \bigl[0\) , \( 0\) , \( 0\) , \( -5042\) , \( 137801\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph