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

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-18000.2-a
• Conductor: 18000.2
• Rank: \( 0 \)

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

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

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

Isogeny class 18000.2-a contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
18000.2-a1	\( \bigl[i + 1\) , \( 1\) , \( 0\) , \( -80 i - 60\) , \( -3300 i - 600\bigr] \)
18000.2-a2	\( \bigl[i + 1\) , \( 1\) , \( 0\) , \( 80 i + 60\) , \( 110 i + 20\bigr] \)
18000.2-a3	\( \bigl[i + 1\) , \( 1\) , \( 0\) , \( -20 i - 15\) , \( 0\bigr] \)
18000.2-a4	\( \bigl[i + 1\) , \( 1\) , \( 0\) , \( -200 i - 150\) , \( -1584 i - 288\bigr] \)
18000.2-a5	\( \bigl[0\) , \( -i - 1\) , \( 0\) , \( 62 i + 46\) , \( -82 i + 259\bigr] \)
18000.2-a6	\( \bigl[i + 1\) , \( 1\) , \( 0\) , \( -3200 i - 2400\) , \( -97284 i - 17688\bigr] \)

Rank

Rank: \( 0 \)

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