Elliptic curve isogeny class 18000.2-g over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-18000.2-g
• Conductor: 18000.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 18000.2-g over \(\Q(\sqrt{-1}) \)

Isogeny class 18000.2-g contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
18000.2-g1	\( \bigl[i + 1\) , \( 1\) , \( 0\) , \( 4 i + 3\) , \( 0\bigr] \)
18000.2-g2	\( \bigl[i + 1\) , \( 1\) , \( 0\) , \( -16 i - 12\) , \( -22 i - 4\bigr] \)
18000.2-g3	\( \bigl[i + 1\) , \( 1\) , \( 0\) , \( -136 i - 102\) , \( 770 i + 140\bigr] \)
18000.2-g4	\( \bigl[i + 1\) , \( 1\) , \( 0\) , \( -216 i - 162\) , \( -1782 i - 324\bigr] \)

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