Elliptic curve isogeny class 4332.2-c over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-4332.2-c
• Conductor: 4332.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 4332.2-c over \(\Q(\sqrt{-3}) \)

Isogeny class 4332.2-c contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
4332.2-c1	\( \bigl[1\) , \( 0\) , \( 0\) , \( -418\) , \( -3610\bigr] \)
4332.2-c2	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 32 a - 32\) , \( 8\bigr] \)
4332.2-c3	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -8 a + 8\) , \( 0\bigr] \)
4332.2-c4	\( \bigl[1\) , \( 0\) , \( 0\) , \( -428\) , \( -3444\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph