Elliptic curve isogeny class 65.3-a over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-65.3-a
• Conductor: 65.3
• Rank: \( 0 \)

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

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

Elliptic curves in class 65.3-a over \(\Q(\sqrt{-1}) \)

Isogeny class 65.3-a contains 6 curves linked by isogenies of degrees dividing 18.

Curve label	Weierstrass Coefficients
65.3-a1	\( \bigl[i + 1\) , \( -i\) , \( i\) , \( -240 i - 399\) , \( 2869 i + 2627\bigr] \)
65.3-a2	\( \bigl[i + 1\) , \( i - 1\) , \( i\) , \( 14 i + 4\) , \( 7 i + 14\bigr] \)
65.3-a3	\( \bigl[i + 1\) , \( i - 1\) , \( i\) , \( -i - 1\) , \( -i + 1\bigr] \)
65.3-a4	\( \bigl[i + 1\) , \( i - 1\) , \( i\) , \( 59 i + 99\) , \( 372 i - 410\bigr] \)
65.3-a5	\( \bigl[i + 1\) , \( -i\) , \( i\) , \( 1\) , \( 0\bigr] \)
65.3-a6	\( \bigl[i + 1\) , \( -i\) , \( i\) , \( -5 i - 4\) , \( 2 i + 5\bigr] \)

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