Elliptic curve isogeny class 67600.6-g over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-67600.6-g
• Conductor: 67600.6
• Rank: \( 1 \)

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

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

Elliptic curves in class 67600.6-g over \(\Q(\sqrt{-1}) \)

Isogeny class 67600.6-g contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
67600.6-g1	\( \bigl[0\) , \( i - 1\) , \( 0\) , \( 42 i - 170\) , \( -394 i + 877\bigr] \)
67600.6-g2	\( \bigl[i + 1\) , \( -1\) , \( i + 1\) , \( 323 i + 464\) , \( -3191 i + 3939\bigr] \)
67600.6-g3	\( \bigl[i + 1\) , \( -1\) , \( i + 1\) , \( 3 i + 49\) , \( 70 i + 101\bigr] \)
67600.6-g4	\( \bigl[i + 1\) , \( -1\) , \( i + 1\) , \( -77 i - 266\) , \( 673 i + 1155\bigr] \)
67600.6-g5	\( \bigl[i + 1\) , \( -1\) , \( i + 1\) , \( -177 i - 1716\) , \( -3817 i - 25925\bigr] \)
67600.6-g6	\( \bigl[i + 1\) , \( -1\) , \( i + 1\) , \( -1257 i - 3856\) , \( 44995 i + 90011\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph