Elliptic curve isogeny class 9604.3-c over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-9604.3-c
• Conductor: 9604.3
• Rank: \( 0 \)

Base field \(\Q(\sqrt{-3}) \)

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

Elliptic curves in class 9604.3-c over \(\Q(\sqrt{-3}) \)

Isogeny class 9604.3-c contains 10 curves linked by isogenies of degrees dividing 18.

Curve label	Weierstrass Coefficients
9604.3-c1	\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 8355 a\) , \( 291341\bigr] \)
9604.3-c2	\( \bigl[1\) , \( 1\) , \( 0\) , \( -25\) , \( -111\bigr] \)
9604.3-c3	\( \bigl[1\) , \( 1\) , \( 0\) , \( 220\) , \( 2192\bigr] \)
9604.3-c4	\( \bigl[1\) , \( 1\) , \( 0\) , \( -1740\) , \( 22184\bigr] \)
9604.3-c5	\( \bigl[1\) , \( 1\) , \( 0\) , \( 11270 a + 9040\) , \( -633570 a + 930252\bigr] \)
9604.3-c6	\( \bigl[1\) , \( 1\) , \( 0\) , \( -11270 a + 20310\) , \( 633570 a + 296682\bigr] \)
9604.3-c7	\( \bigl[1\) , \( 1\) , \( 0\) , \( -515\) , \( -4717\bigr] \)
9604.3-c8	\( \bigl[1\) , \( 1\) , \( 0\) , \( 10780 a + 9040\) , \( -647780 a + 987876\bigr] \)
9604.3-c9	\( \bigl[1\) , \( 1\) , \( 0\) , \( -10780 a + 19820\) , \( 647780 a + 340096\bigr] \)
9604.3-c10	\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 133795 a\) , \( 18781197\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph