Elliptic curve isogeny class 340.4-a over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-340.4-a
• Conductor: 340.4
• Rank: \( 0 \)

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

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

Elliptic curves in class 340.4-a over \(\Q(\sqrt{-1}) \)

Isogeny class 340.4-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
340.4-a1	\( \bigl[i + 1\) , \( i + 1\) , \( 0\) , \( -6 i - 19\) , \( -2 i + 25\bigr] \)
340.4-a2	\( \bigl[0\) , \( i\) , \( 0\) , \( -2 i - 1\) , \( -i + 1\bigr] \)
340.4-a3	\( \bigl[0\) , \( i\) , \( 0\) , \( 18 i + 19\) , \( -13 i + 41\bigr] \)
340.4-a4	\( \bigl[i + 1\) , \( i + 1\) , \( 0\) , \( 4 i + 1\) , \( 2 i + 1\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 6 & 2 & 3 \\ 6 & 1 & 3 & 2 \\ 2 & 3 & 1 & 6 \\ 3 & 2 & 6 & 1 \end{array}\right)\)

Isogeny graph