Elliptic curve isogeny class 22050.2-c over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-22050.2-c
• Conductor: 22050.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 22050.2-c over \(\Q(\sqrt{-1}) \)

Isogeny class 22050.2-c contains 8 curves linked by isogenies of degrees dividing 12.

Curve label	Weierstrass Coefficients
22050.2-c1	\( \bigl[i\) , \( 0\) , \( 0\) , \( -81\) , \( -6561\bigr] \)
22050.2-c2	\( \bigl[i\) , \( 0\) , \( 0\) , \( 729\) , \( 176985\bigr] \)
22050.2-c3	\( \bigl[i\) , \( 0\) , \( 0\) , \( -41\) , \( 39\bigr] \)
22050.2-c4	\( \bigl[i\) , \( 0\) , \( 0\) , \( -6451\) , \( -124931\bigr] \)
22050.2-c5	\( \bigl[i\) , \( 0\) , \( 0\) , \( -2701\) , \( 52819\bigr] \)
22050.2-c6	\( \bigl[i\) , \( 0\) , \( 0\) , \( -361\) , \( -2585\bigr] \)
22050.2-c7	\( \bigl[i\) , \( 0\) , \( 0\) , \( -2681\) , \( 53655\bigr] \)
22050.2-c8	\( \bigl[i\) , \( 0\) , \( 0\) , \( -5761\) , \( -167825\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 3 & 4 & 12 & 6 & 2 & 12 & 4 \\ 3 & 1 & 12 & 4 & 2 & 6 & 4 & 12 \\ 4 & 12 & 1 & 12 & 6 & 2 & 3 & 4 \\ 12 & 4 & 12 & 1 & 2 & 6 & 4 & 3 \\ 6 & 2 & 6 & 2 & 1 & 3 & 2 & 6 \\ 2 & 6 & 2 & 6 & 3 & 1 & 6 & 2 \\ 12 & 4 & 3 & 4 & 2 & 6 & 1 & 12 \\ 4 & 12 & 4 & 3 & 6 & 2 & 12 & 1 \end{array}\right)\)

Isogeny graph