Elliptic curve isogeny class 43.1-a over number field 3.3.321.1

• Base field: 3.3.321.1
• Label: 3.3.321.1-43.1-a
• Conductor: 43.1
• Rank: \( 0 \)

Base field 3.3.321.1

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

Elliptic curves in class 43.1-a over 3.3.321.1

Isogeny class 43.1-a contains 3 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
43.1-a1	\( \bigl[a^{2} - a - 3\) , \( -a - 1\) , \( a\) , \( -911 a^{2} - 853 a + 257\) , \( -24109 a^{2} - 40625 a + 11093\bigr] \)
43.1-a2	\( \bigl[a^{2} - a - 2\) , \( -a^{2} + a + 3\) , \( a^{2} - a - 3\) , \( -38894 a^{2} + 105008 a - 22883\) , \( 8383982 a^{2} - 22633861 a + 4932888\bigr] \)
43.1-a3	\( \bigl[a^{2} - 2\) , \( a^{2} - 4\) , \( a\) , \( -37 a^{2} - 85 a - 3\) , \( -469 a^{2} - 747 a + 174\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 3 & 3 \\ 3 & 1 & 9 \\ 3 & 9 & 1 \end{array}\right)\)

Isogeny graph