Elliptic curve isogeny class 9.2-a over number field 3.3.321.1

• Base field: 3.3.321.1
• Label: 3.3.321.1-9.2-a
• Conductor: 9.2
• 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 9.2-a over 3.3.321.1

Isogeny class 9.2-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
9.2-a1	\( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( 660 a^{2} - 490 a - 2793\) , \( -14053 a^{2} + 10729 a + 58676\bigr] \)
9.2-a2	\( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( -30 a^{2} + 220 a - 363\) , \( -1063 a^{2} + 3089 a - 1168\bigr] \)
9.2-a3	\( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( 35 a^{2} - 15 a - 178\) , \( -252 a^{2} + 231 a + 954\bigr] \)
9.2-a4	\( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( -3\) , \( -9 a^{2} + 7 a + 34\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph