Elliptic curve isogeny class 43776.1-q over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-43776.1-q
• Conductor: 43776.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 43776.1-q over \(\Q(\sqrt{-3}) \)

Isogeny class 43776.1-q contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
43776.1-q1	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 25 a + 25\) , \( -63 a + 136\bigr] \)
43776.1-q2	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 105 a - 135\) , \( -847 a + 504\bigr] \)
43776.1-q3	\( \bigl[0\) , \( 0\) , \( 0\) , \( -24 a - 15\) , \( 12 a + 30\bigr] \)
43776.1-q4	\( \bigl[0\) , \( 0\) , \( 0\) , \( -264 a - 255\) , \( 3036 a + 1038\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph