Elliptic curve isogeny class 43776.2-l over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-43776.2-l
• Conductor: 43776.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 43776.2-l over \(\Q(\sqrt{-3}) \)

Isogeny class 43776.2-l contains 4 curves linked by isogenies of degrees dividing 10.

Curve label	Weierstrass Coefficients
43776.2-l1	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -1710 a - 5049\) , \( 225441 a + 82071\bigr] \)
43776.2-l2	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -30 a - 9\) , \( -15 a - 249\bigr] \)
43776.2-l3	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -1710 a + 2631\) , \( 16545 a + 34455\bigr] \)
43776.2-l4	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 450 a - 9\) , \( 81 a - 3321\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 10 & 2 & 5 \\ 10 & 1 & 5 & 2 \\ 2 & 5 & 1 & 10 \\ 5 & 2 & 10 & 1 \end{array}\right)\)

Isogeny graph