Elliptic curve isogeny class 1105.7-a over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-1105.7-a
• Conductor: 1105.7
• Rank: \( 0 \)

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

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

Elliptic curves in class 1105.7-a over \(\Q(\sqrt{-1}) \)

Isogeny class 1105.7-a contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
1105.7-a1	\( \bigl[i\) , \( -i - 1\) , \( i + 1\) , \( -2 i + 2\) , \( -3\bigr] \)
1105.7-a2	\( \bigl[i\) , \( -i - 1\) , \( i + 1\) , \( 38 i - 8\) , \( -102 i - 17\bigr] \)
1105.7-a3	\( \bigl[i\) , \( -i - 1\) , \( i + 1\) , \( -2 i - 3\) , \( -3 i - 5\bigr] \)
1105.7-a4	\( \bigl[i\) , \( -i - 1\) , \( i + 1\) , \( -47 i - 98\) , \( -92 i - 72\bigr] \)
1105.7-a5	\( \bigl[i\) , \( -i - 1\) , \( i + 1\) , \( -42 i - 78\) , \( -176 i - 221\bigr] \)
1105.7-a6	\( \bigl[i\) , \( -i - 1\) , \( i + 1\) , \( -677 i - 1258\) , \( -13332 i - 15054\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph