Elliptic curve isogeny class 130.4-a over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-130.4-a
• Conductor: 130.4
• Rank: \( 0 \)

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

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

Elliptic curves in class 130.4-a over \(\Q(\sqrt{-1}) \)

Isogeny class 130.4-a contains 6 curves linked by isogenies of degrees dividing 18.

Curve label	Weierstrass Coefficients
130.4-a1	\( \bigl[i\) , \( i + 1\) , \( i\) , \( -89 i - 50\) , \( 368 i + 14\bigr] \)
130.4-a2	\( \bigl[i\) , \( i + 1\) , \( i\) , \( -9 i + 5\) , \( -2 i + 18\bigr] \)
130.4-a3	\( \bigl[i\) , \( i + 1\) , \( i\) , \( i + 15\) , \( -30 i + 30\bigr] \)
130.4-a4	\( \bigl[i\) , \( i + 1\) , \( i\) , \( -9 i - 130\) , \( 688 i - 882\bigr] \)
130.4-a5	\( \bigl[i\) , \( i + 1\) , \( i\) , \( i\) , \( 0\bigr] \)
130.4-a6	\( \bigl[i\) , \( i + 1\) , \( i\) , \( 6 i - 5\) , \( -8 i\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph