Elliptic curve isogeny class 16200.2-d over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-16200.2-d
• Conductor: 16200.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 16200.2-d over \(\Q(\sqrt{-1}) \)

Isogeny class 16200.2-d contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
16200.2-d1	\( \bigl[i + 1\) , \( i\) , \( i + 1\) , \( -i - 9\) , \( -9 i\bigr] \)
16200.2-d2	\( \bigl[i + 1\) , \( i\) , \( i + 1\) , \( -i + 36\) , \( -18 i\bigr] \)
16200.2-d3	\( \bigl[i + 1\) , \( i\) , \( i + 1\) , \( -i + 306\) , \( 2196 i\bigr] \)
16200.2-d4	\( \bigl[i + 1\) , \( i\) , \( i + 1\) , \( -i + 486\) , \( -3888 i\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph