Elliptic curve isogeny class 57800.4-c over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-57800.4-c
• Conductor: 57800.4
• Rank: \( 1 \)

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

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

Elliptic curves in class 57800.4-c over \(\Q(\sqrt{-1}) \)

Isogeny class 57800.4-c contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
57800.4-c1	\( \bigl[i + 1\) , \( i + 1\) , \( 0\) , \( -6933 i + 6265\) , \( 109144 i + 335983\bigr] \)
57800.4-c2	\( \bigl[i + 1\) , \( i + 1\) , \( 0\) , \( -433 i + 390\) , \( 1769 i + 5508\bigr] \)
57800.4-c3	\( \bigl[i + 1\) , \( i + 1\) , \( 0\) , \( 5887 i + 7905\) , \( -212070 i + 307155\bigr] \)
57800.4-c4	\( \bigl[i + 1\) , \( i + 1\) , \( 0\) , \( -13 i + 455\) , \( -1940 i + 12245\bigr] \)
57800.4-c5	\( \bigl[0\) , \( -i\) , \( 0\) , \( 216 i - 77\) , \( 261 i + 979\bigr] \)
57800.4-c6	\( \bigl[i + 1\) , \( i + 1\) , \( 0\) , \( 807 i - 5955\) , \( -37466 i + 157543\bigr] \)

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