Elliptic curve isogeny class 5329.3-a over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-5329.3-a
• Conductor: 5329.3
• Rank: \( 1 \)

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

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

Elliptic curves in class 5329.3-a over \(\Q(\sqrt{-3}) \)

Isogeny class 5329.3-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
5329.3-a1	\( \bigl[a\) , \( a - 1\) , \( a + 1\) , \( -555 a + 1090\) , \( -8540 a - 3747\bigr] \)
5329.3-a2	\( \bigl[1\) , \( 1\) , \( a + 1\) , \( -341 a - 76\) , \( -3390 a + 857\bigr] \)
5329.3-a3	\( \bigl[1\) , \( 1\) , \( a + 1\) , \( -26 a + 9\) , \( -72 a - 24\bigr] \)
5329.3-a4	\( \bigl[a\) , \( a - 1\) , \( a + 1\) , \( -870 a + 1005\) , \( -17501 a + 5508\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph