Elliptic curve isogeny class 20808.2-c over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-20808.2-c
• Conductor: 20808.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 20808.2-c over \(\Q(\sqrt{-1}) \)

Isogeny class 20808.2-c contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
20808.2-c1	\( \bigl[i + 1\) , \( 0\) , \( 0\) , \( -72\) , \( -36 i\bigr] \)
20808.2-c2	\( \bigl[i + 1\) , \( 0\) , \( 0\) , \( 18\) , \( 0\bigr] \)
20808.2-c3	\( \bigl[i + 1\) , \( 0\) , \( 0\) , \( 188\) , \( 1020 i\bigr] \)
20808.2-c4	\( \bigl[i + 1\) , \( 0\) , \( 0\) , \( 13\) , \( -16 i\bigr] \)

Rank

Rank: \( 0 \)

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