Elliptic curve isogeny class 290.3-a over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-290.3-a
• Conductor: 290.3
• Rank: \( 0 \)

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

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

Elliptic curves in class 290.3-a over \(\Q(\sqrt{-1}) \)

Isogeny class 290.3-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
290.3-a1	\( \bigl[1\) , \( 1\) , \( i\) , \( -25 i + 16\) , \( 10 i + 121\bigr] \)
290.3-a2	\( \bigl[i\) , \( -1\) , \( 1\) , \( 1\) , \( -1\bigr] \)
290.3-a3	\( \bigl[1\) , \( 1\) , \( i\) , \( 10 i + 11\) , \( -4 i + 25\bigr] \)
290.3-a4	\( \bigl[i\) , \( -1\) , \( 1\) , \( -30 i + 21\) , \( 2 i - 91\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 6 & 3 & 2 \\ 6 & 1 & 2 & 3 \\ 3 & 2 & 1 & 6 \\ 2 & 3 & 6 & 1 \end{array}\right)\)

Isogeny graph