Elliptic curve isogeny class 43.2-a over number field 6.6.434581.1

• Base field: 6.6.434581.1
• Label: 6.6.434581.1-43.2-a
• Conductor: 43.2
• Rank: \( 0 \)

Base field 6.6.434581.1

Generator \(a\), with minimal polynomial \( x^{6} - 2 x^{5} - 4 x^{4} + 5 x^{3} + 4 x^{2} - 2 x - 1 \); class number \(1\).

Elliptic curves in class 43.2-a over 6.6.434581.1

Isogeny class 43.2-a contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
43.2-a1	\( \bigl[a^{5} - a^{4} - 5 a^{3} + a^{2} + 3 a\) , \( a^{5} - 4 a^{4} + 11 a^{2} - 3 a - 4\) , \( 2 a^{5} - 5 a^{4} - 5 a^{3} + 12 a^{2} - 3\) , \( -3 a^{5} + 2 a^{4} + 16 a^{3} + 2 a^{2} - 9 a - 1\) , \( 9 a^{5} - 24 a^{4} - 27 a^{3} + 71 a^{2} + 19 a - 34\bigr] \)
43.2-a2	\( \bigl[2 a^{5} - 4 a^{4} - 6 a^{3} + 7 a^{2} + 2 a - 1\) , \( a^{3} - a^{2} - 2 a + 1\) , \( a^{5} - 2 a^{4} - 3 a^{3} + 3 a^{2} + a\) , \( 11 a^{5} - 13 a^{4} - 46 a^{3} + 7 a^{2} + 22 a + 6\) , \( 28 a^{5} - 24 a^{4} - 131 a^{3} - 19 a^{2} + 61 a + 20\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph