Elliptic curve isogeny class 13689.3-CMb over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-13689.3-CMb
• Conductor: 13689.3
• Rank: \( 0 \)

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

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

Elliptic curves in class 13689.3-CMb over \(\Q(\sqrt{-3}) \)

Isogeny class 13689.3-CMb contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
13689.3-CMb1	\( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( -9 a + 13\bigr] \)
13689.3-CMb2	\( \bigl[0\) , \( 0\) , \( 1\) , \( 210 a - 450\) , \( -2277 a + 3352\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph