Elliptic curve isogeny class 65.2-a over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-65.2-a
• Conductor: 65.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 65.2-a over \(\Q(\sqrt{-1}) \)

Isogeny class 65.2-a contains 6 curves linked by isogenies of degrees dividing 18.

Curve label	Weierstrass Coefficients
65.2-a1	\( \bigl[i + 1\) , \( 0\) , \( i\) , \( 239 i - 399\) , \( -2869 i + 2627\bigr] \)
65.2-a2	\( \bigl[i + 1\) , \( i + 1\) , \( 1\) , \( -15 i + 3\) , \( 7 i - 14\bigr] \)
65.2-a3	\( \bigl[i + 1\) , \( i + 1\) , \( 1\) , \( -2\) , \( -i - 1\bigr] \)
65.2-a4	\( \bigl[i + 1\) , \( i + 1\) , \( 1\) , \( -60 i + 98\) , \( 372 i + 410\bigr] \)
65.2-a5	\( \bigl[i + 1\) , \( 0\) , \( i\) , \( -i + 1\) , \( 0\bigr] \)
65.2-a6	\( \bigl[i + 1\) , \( 0\) , \( i\) , \( 4 i - 4\) , \( -2 i + 5\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph