Elliptic curve isogeny class 13520.1-b over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-13520.1-b
• Conductor: 13520.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 13520.1-b over \(\Q(\sqrt{-1}) \)

Isogeny class 13520.1-b contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
13520.1-b1	\( \bigl[i + 1\) , \( -1\) , \( 0\) , \( 66 i - 18\) , \( 190 i + 80\bigr] \)
13520.1-b2	\( \bigl[i + 1\) , \( -1\) , \( 0\) , \( -774 i + 332\) , \( -3058 i + 9320\bigr] \)
13520.1-b3	\( \bigl[i + 1\) , \( -1\) , \( 0\) , \( 16 i - 138\) , \( 126 i + 1008\bigr] \)
13520.1-b4	\( \bigl[i + 1\) , \( -1\) , \( 0\) , \( 6 i + 7\) , \( 10 i - 14\bigr] \)
13520.1-b5	\( \bigl[i + 1\) , \( -1\) , \( 0\) , \( 6 i - 2528\) , \( -626 i + 49768\bigr] \)
13520.1-b6	\( \bigl[i + 1\) , \( -1\) , \( 0\) , \( 1076 i - 298\) , \( 12934 i + 5248\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph