Elliptic curve isogeny class 1010.4-a over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-1010.4-a
• Conductor: 1010.4
• Rank: \( 0 \)

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

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

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph

Elliptic curves in class 1010.4-a over \(\Q(\sqrt{-1}) \)

Isogeny class 1010.4-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
1010.4-a1	\( \bigl[i\) , \( i + 1\) , \( 1\) , \( 32 i - 35\) , \( 109 i - 75\bigr] \)
1010.4-a2	\( \bigl[i\) , \( i + 1\) , \( 1\) , \( 2 i\) , \( -2\bigr] \)
1010.4-a3	\( \bigl[i\) , \( i + 1\) , \( 1\) , \( -3 i + 5\) , \( -6 i - 2\bigr] \)
1010.4-a4	\( \bigl[i\) , \( i + 1\) , \( 1\) , \( 22 i - 45\) , \( 137 i - 3\bigr] \)