Elliptic curve isogeny class 24.1-b over number field 3.3.321.1

• Base field: 3.3.321.1
• Label: 3.3.321.1-24.1-b
• Conductor: 24.1
• 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 24.1-b over 3.3.321.1

Isogeny class 24.1-b contains 3 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
24.1-b1	\( \bigl[a^{2} - a - 3\) , \( -a - 1\) , \( a\) , \( -319 a^{2} - 476 a + 133\) , \( -18887 a^{2} - 27538 a + 7665\bigr] \)
24.1-b2	\( \bigl[a^{2} - a - 3\) , \( -a - 1\) , \( a\) , \( -37934 a^{2} - 54796 a + 15273\) , \( -8554625 a^{2} - 12485773 a + 3474792\bigr] \)
24.1-b3	\( \bigl[a^{2} - a - 3\) , \( -a^{2} + 2 a + 3\) , \( a\) , \( -3 a^{2} + 4 a + 9\) , \( 5 a^{2} - 16 a + 8\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph