Elliptic curve isogeny class 57800.6-b over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-57800.6-b
• Conductor: 57800.6
• Rank: \( 1 \)

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

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

Elliptic curves in class 57800.6-b over \(\Q(\sqrt{-1}) \)

Isogeny class 57800.6-b contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
57800.6-b1	\( \bigl[i + 1\) , \( i - 1\) , \( 0\) , \( 6933 i + 6265\) , \( 109144 i - 335983\bigr] \)
57800.6-b2	\( \bigl[i + 1\) , \( i - 1\) , \( 0\) , \( 433 i + 390\) , \( 1769 i - 5508\bigr] \)
57800.6-b3	\( \bigl[i + 1\) , \( i - 1\) , \( 0\) , \( -5887 i + 7905\) , \( -212070 i - 307155\bigr] \)
57800.6-b4	\( \bigl[i + 1\) , \( i - 1\) , \( 0\) , \( 13 i + 455\) , \( -1940 i - 12245\bigr] \)
57800.6-b5	\( \bigl[0\) , \( i\) , \( 0\) , \( -216 i - 77\) , \( -261 i + 979\bigr] \)
57800.6-b6	\( \bigl[i + 1\) , \( i - 1\) , \( 0\) , \( -807 i - 5955\) , \( -37466 i - 157543\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph