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

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

Isogeny class 12544.2-c contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
12544.2-c1	\( \bigl[0\) , \( -a\) , \( 0\) , \( 12 a + 4\) , \( -12 a + 28\bigr] \)
12544.2-c2	\( \bigl[0\) , \( -a\) , \( 0\) , \( 12 a - 36\) , \( -92 a + 140\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph