Elliptic curve isogeny class 20808.1-a over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-20808.1-a
• Conductor: 20808.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 20808.1-a over \(\Q(\sqrt{-1}) \)

Isogeny class 20808.1-a contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
20808.1-a1	\( \bigl[i + 1\) , \( -i + 1\) , \( 0\) , \( 31 i + 59\) , \( -1026 i - 1111\bigr] \)
20808.1-a2	\( \bigl[0\) , \( i - 1\) , \( 0\) , \( -6 i - 10\) , \( 12 i - 7\bigr] \)
20808.1-a3	\( \bigl[i + 1\) , \( -i + 1\) , \( 0\) , \( -9 i - 16\) , \( 15 i + 10\bigr] \)
20808.1-a4	\( \bigl[i + 1\) , \( -i + 1\) , \( 0\) , \( -49 i - 91\) , \( -260 i - 325\bigr] \)
20808.1-a5	\( \bigl[i + 1\) , \( -1\) , \( 0\) , \( -129 i - 241\) , \( -1164 i - 1189\bigr] \)
20808.1-a6	\( \bigl[i + 1\) , \( -i + 1\) , \( 0\) , \( -769 i - 1441\) , \( -17054 i - 19459\bigr] \)

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