Elliptic curve isogeny class 3600.1-c over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-3600.1-c
• Conductor: 3600.1
• Rank: \( 0 \)

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

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

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph

Elliptic curves in class 3600.1-c over \(\Q(\sqrt{-1}) \)

Isogeny class 3600.1-c contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
3600.1-c1	\( \bigl[i + 1\) , \( -i - 1\) , \( i + 1\) , \( 15 i + 12\) , \( -248 i - 45\bigr] \)
3600.1-c2	\( \bigl[0\) , \( -i - 1\) , \( 0\) , \( -2 i - 2\) , \( 2 i - 3\bigr] \)
3600.1-c3	\( \bigl[i + 1\) , \( -i - 1\) , \( i + 1\) , \( -5 i - 3\) , \( 5 i + 1\bigr] \)
3600.1-c4	\( \bigl[i + 1\) , \( 1\) , \( i + 1\) , \( -25 i - 18\) , \( 49 i + 9\bigr] \)
3600.1-c5	\( \bigl[i + 1\) , \( -i - 1\) , \( i + 1\) , \( -65 i - 48\) , \( 302 i + 55\bigr] \)
3600.1-c6	\( \bigl[i + 1\) , \( 1\) , \( i + 1\) , \( -385 i - 288\) , \( 3811 i + 693\bigr] \)