Elliptic curve isogeny class 1040.3-a over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-1040.3-a
• Conductor: 1040.3
• Rank: \( 0 \)

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

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

Elliptic curves in class 1040.3-a over \(\Q(\sqrt{-1}) \)

Isogeny class 1040.3-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
1040.3-a1	\( \bigl[i + 1\) , \( 1\) , \( i + 1\) , \( 9 i + 6\) , \( 3 i + 15\bigr] \)
1040.3-a2	\( \bigl[i + 1\) , \( -i - 1\) , \( i + 1\) , \( -i + 1\) , \( -i - 1\bigr] \)
1040.3-a3	\( \bigl[0\) , \( -i - 1\) , \( 0\) , \( 2 i + 2\) , \( -2 i + 1\bigr] \)
1040.3-a4	\( \bigl[i + 1\) , \( -i - 1\) , \( i + 1\) , \( -11 i + 16\) , \( -20 i - 31\bigr] \)

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