Elliptic curve isogeny class 12544.2-k over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-12544.2-k
• Conductor: 12544.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 12544.2-k over \(\Q(\sqrt{-3}) \)

Isogeny class 12544.2-k contains 10 curves linked by isogenies of degrees dividing 18.

Curve label	Weierstrass Coefficients
12544.2-k1	\( \bigl[0\) , \( -1\) , \( 0\) , \( -2728\) , \( 55920\bigr] \)
12544.2-k2	\( \bigl[0\) , \( -1\) , \( 0\) , \( -8\) , \( -16\bigr] \)
12544.2-k3	\( \bigl[0\) , \( -1\) , \( 0\) , \( 72\) , \( 368\bigr] \)
12544.2-k4	\( \bigl[0\) , \( -1\) , \( 0\) , \( -568\) , \( 4464\bigr] \)
12544.2-k5	\( \bigl[0\) , \( -1\) , \( 0\) , \( -3680 a + 6632\) , \( 120320 a + 51568\bigr] \)
12544.2-k6	\( \bigl[0\) , \( -1\) , \( 0\) , \( 3680 a + 2952\) , \( -120320 a + 171888\bigr] \)
12544.2-k7	\( \bigl[0\) , \( -1\) , \( 0\) , \( -168\) , \( -784\bigr] \)
12544.2-k8	\( \bigl[0\) , \( -1\) , \( 0\) , \( -3520 a + 6472\) , \( 122880 a + 59760\bigr] \)
12544.2-k9	\( \bigl[0\) , \( -1\) , \( 0\) , \( 3520 a + 2952\) , \( -122880 a + 182640\bigr] \)
12544.2-k10	\( \bigl[0\) , \( -1\) , \( 0\) , \( -43688\) , \( 3529328\bigr] \)

Rank

Rank: \( 1 \)

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