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

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-12544.2-e
• 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-e over \(\Q(\sqrt{-3}) \)

Isogeny class 12544.2-e contains 8 curves linked by isogenies of degrees dividing 12.

Curve label	Weierstrass Coefficients
12544.2-e1	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 88 a - 1624\) , \( -2480 a + 24592\bigr] \)
12544.2-e2	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 74 a + 63\) , \( -359 a - 1441\bigr] \)
12544.2-e3	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -72 a + 136\) , \( -432 a + 1936\bigr] \)
12544.2-e4	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -6 a - 17\) , \( 9 a + 15\bigr] \)
12544.2-e5	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 8 a - 104\) , \( -48 a + 336\bigr] \)
12544.2-e6	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 8 a - 24\) , \( 16 a - 48\bigr] \)
12544.2-e7	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -6 a - 97\) , \( -55 a - 385\bigr] \)
12544.2-e8	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -86 a - 1537\) , \( -2567 a - 23649\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 3 & 4 & 12 & 2 & 4 & 6 & 12 \\ 3 & 1 & 12 & 4 & 6 & 12 & 2 & 4 \\ 4 & 12 & 1 & 12 & 2 & 4 & 6 & 3 \\ 12 & 4 & 12 & 1 & 6 & 3 & 2 & 4 \\ 2 & 6 & 2 & 6 & 1 & 2 & 3 & 6 \\ 4 & 12 & 4 & 3 & 2 & 1 & 6 & 12 \\ 6 & 2 & 6 & 2 & 3 & 6 & 1 & 2 \\ 12 & 4 & 3 & 4 & 6 & 12 & 2 & 1 \end{array}\right)\)

Isogeny graph