Elliptic curve isogeny class 19600.1-b over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-19600.1-b
• Conductor: 19600.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 19600.1-b over \(\Q(\sqrt{-1}) \)

Isogeny class 19600.1-b contains 6 curves linked by isogenies of degrees dividing 18.

Curve label	Weierstrass Coefficients
19600.1-b1	\( \bigl[i + 1\) , \( -i - 1\) , \( 0\) , \( -2728 i - 2046\) , \( 76890 i + 13980\bigr] \)
19600.1-b2	\( \bigl[i + 1\) , \( -i - 1\) , \( 0\) , \( -8 i - 6\) , \( -22 i - 4\bigr] \)
19600.1-b3	\( \bigl[i + 1\) , \( -i - 1\) , \( 0\) , \( 72 i + 54\) , \( 506 i + 92\bigr] \)
19600.1-b4	\( \bigl[i + 1\) , \( -i - 1\) , \( 0\) , \( -568 i - 426\) , \( 6138 i + 1116\bigr] \)
19600.1-b5	\( \bigl[i + 1\) , \( -i - 1\) , \( 0\) , \( -168 i - 126\) , \( -1078 i - 196\bigr] \)
19600.1-b6	\( \bigl[i + 1\) , \( -i - 1\) , \( 0\) , \( -43688 i - 32766\) , \( 4852826 i + 882332\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 9 & 3 & 6 & 18 & 2 \\ 9 & 1 & 3 & 6 & 2 & 18 \\ 3 & 3 & 1 & 2 & 6 & 6 \\ 6 & 6 & 2 & 1 & 3 & 3 \\ 18 & 2 & 6 & 3 & 1 & 9 \\ 2 & 18 & 6 & 3 & 9 & 1 \end{array}\right)\)

Isogeny graph