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

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-22050.2-d
• 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-d over \(\Q(\sqrt{-1}) \)

Isogeny class 22050.2-d contains 10 curves linked by isogenies of degrees dividing 16.

Curve label	Weierstrass Coefficients
22050.2-d1	\( \bigl[i\) , \( 0\) , \( 0\) , \( -119300\) , \( 16229850\bigr] \)
22050.2-d2	\( \bigl[i\) , \( 0\) , \( 0\) , \( 1270\) , \( 789048\bigr] \)
22050.2-d3	\( \bigl[i\) , \( 0\) , \( 0\) , \( 210\) , \( -900\bigr] \)
22050.2-d4	\( \bigl[i\) , \( 0\) , \( 0\) , \( -1070\) , \( -7812\bigr] \)
22050.2-d5	\( \bigl[i\) , \( 0\) , \( 0\) , \( -7550\) , \( 247500\bigr] \)
22050.2-d6	\( \bigl[i\) , \( 0\) , \( 0\) , \( 110670 i + 71830\) , \( -1502718 i + 18136224\bigr] \)
22050.2-d7	\( \bigl[i\) , \( 0\) , \( 0\) , \( -110670 i + 71830\) , \( 1502718 i + 18136224\bigr] \)
22050.2-d8	\( \bigl[i\) , \( 0\) , \( 0\) , \( -15070\) , \( -710612\bigr] \)
22050.2-d9	\( \bigl[i\) , \( 0\) , \( 0\) , \( -120050\) , \( 16020000\bigr] \)
22050.2-d10	\( \bigl[i\) , \( 0\) , \( 0\) , \( -1920800\) , \( 1024800150\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrrrr} 1 & 8 & 16 & 8 & 4 & 16 & 16 & 16 & 2 & 4 \\ 8 & 1 & 8 & 4 & 2 & 2 & 2 & 8 & 4 & 8 \\ 16 & 8 & 1 & 2 & 4 & 16 & 16 & 4 & 8 & 16 \\ 8 & 4 & 2 & 1 & 2 & 8 & 8 & 2 & 4 & 8 \\ 4 & 2 & 4 & 2 & 1 & 4 & 4 & 4 & 2 & 4 \\ 16 & 2 & 16 & 8 & 4 & 1 & 4 & 16 & 8 & 16 \\ 16 & 2 & 16 & 8 & 4 & 4 & 1 & 16 & 8 & 16 \\ 16 & 8 & 4 & 2 & 4 & 16 & 16 & 1 & 8 & 16 \\ 2 & 4 & 8 & 4 & 2 & 8 & 8 & 8 & 1 & 2 \\ 4 & 8 & 16 & 8 & 4 & 16 & 16 & 16 & 2 & 1 \end{array}\right)\)

Isogeny graph