Elliptic curve isogeny class 4913.3-a over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-4913.3-a
• Conductor: 4913.3
• Rank: \( 0 \)

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

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

Elliptic curves in class 4913.3-a over \(\Q(\sqrt{-1}) \)

Isogeny class 4913.3-a contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
4913.3-a1	\( \bigl[i\) , \( 1\) , \( i + 1\) , \( -6 i + 11\) , \( -725 i - 651\bigr] \)
4913.3-a2	\( \bigl[i\) , \( 1\) , \( i + 1\) , \( -6 i + 11\) , \( 3 i + 7\bigr] \)
4913.3-a3	\( \bigl[i\) , \( 1\) , \( i + 1\) , \( 1439 i + 11\) , \( -14019 i - 14812\bigr] \)
4913.3-a4	\( \bigl[i\) , \( 1\) , \( i + 1\) , \( -811 i - 1189\) , \( -16391 i - 13110\bigr] \)
4913.3-a5	\( \bigl[1\) , \( -1\) , \( i + 1\) , \( -46 i + 85\) , \( 279 i + 221\bigr] \)
4913.3-a6	\( \bigl[1\) , \( -1\) , \( i + 1\) , \( -726 i + 1360\) , \( 17466 i + 15283\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph