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

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

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

Curve label	Weierstrass Coefficients
12544.2-i1	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -62 a + 23\) , \( 121 a - 133\bigr] \)
12544.2-i2	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -22 a + 63\) , \( 161 a + 35\bigr] \)
12544.2-i3	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -2 a + 3\) , \( 5 a - 1\bigr] \)
12544.2-i4	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 3 a - 2\) , \( 2 a - 2\bigr] \)

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