Elliptic curve isogeny class 33124.9-a over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-33124.9-a
• Conductor: 33124.9
• Rank: \( 1 \)

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

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

Elliptic curves in class 33124.9-a over \(\Q(\sqrt{-3}) \)

Isogeny class 33124.9-a contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
33124.9-a1	\( \bigl[1\) , \( -a\) , \( 1\) , \( -2 a\) , \( -a + 2\bigr] \)
33124.9-a2	\( \bigl[1\) , \( -a\) , \( 1\) , \( -22 a - 115\) , \( 187 a + 446\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph