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

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-57800.6-g
• Conductor: 57800.6
• Rank: \( 0 \)

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

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

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

Isogeny class 57800.6-g contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
57800.6-g1	\( \bigl[i + 1\) , \( -i - 1\) , \( 0\) , \( -83 i + 12\) , \( -91 i - 28\bigr] \)
57800.6-g2	\( \bigl[0\) , \( i + 1\) , \( 0\) , \( -86 i + 18\) , \( -16 i - 85\bigr] \)
57800.6-g3	\( \bigl[i + 1\) , \( -i - 1\) , \( 0\) , \( -813 i + 297\) , \( 2696 i - 9697\bigr] \)
57800.6-g4	\( \bigl[i + 1\) , \( -i - 1\) , \( 0\) , \( -1033 i - 13\) , \( -8876 i + 8677\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph