Elliptic curve isogeny class 1800.2-a over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-1800.2-a
• Conductor: 1800.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 1800.2-a over \(\Q(\sqrt{-1}) \)

Isogeny class 1800.2-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
1800.2-a1	\( \bigl[i + 1\) , \( -i\) , \( 0\) , \( -1\) , \( 0\bigr] \)
1800.2-a2	\( \bigl[i + 1\) , \( -i\) , \( 0\) , \( 4\) , \( -2 i\bigr] \)
1800.2-a3	\( \bigl[i + 1\) , \( -i\) , \( 0\) , \( 34\) , \( 70 i\bigr] \)
1800.2-a4	\( \bigl[i + 1\) , \( -i\) , \( 0\) , \( 54\) , \( -162 i\bigr] \)

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