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

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-12544.2-d
• Conductor: 12544.2
• Rank: \( 0 \)

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

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

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

Isogeny class 12544.2-d contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
12544.2-d1	\( \bigl[0\) , \( 0\) , \( 0\) , \( -15 a + 7\) , \( 16 a - 22\bigr] \)
12544.2-d2	\( \bigl[0\) , \( 0\) , \( 0\) , \( 15 a - 8\) , \( 16 a + 6\bigr] \)
12544.2-d3	\( \bigl[0\) , \( 0\) , \( 0\) , \( 2\) , \( 2 a - 1\bigr] \)
12544.2-d4	\( \bigl[0\) , \( 0\) , \( 0\) , \( 37\) , \( 100 a - 50\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph