Elliptic curve isogeny class 9.3-a over number field 3.3.321.1

• Base field: 3.3.321.1
• Label: 3.3.321.1-9.3-a
• Conductor: 9.3
• 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 9.3-a over 3.3.321.1

Isogeny class 9.3-a contains 3 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
9.3-a1	\( \bigl[0\) , \( a^{2} - a - 2\) , \( a^{2} - 3\) , \( -708 a^{2} - 719 a + 214\) , \( -19813 a^{2} - 25500 a + 7228\bigr] \)
9.3-a2	\( \bigl[0\) , \( a^{2} - a - 2\) , \( a + 1\) , \( 2 a^{2} - 38 a - 70\) , \( 73 a^{2} + 280 a + 265\bigr] \)
9.3-a3	\( \bigl[0\) , \( -a - 1\) , \( a^{2} - a - 3\) , \( 2354 a^{2} + 3433 a - 955\) , \( -230385 a^{2} - 336480 a + 93631\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph