Elliptic curve isogeny class 9.2-b over number field 3.3.257.1

• Base field: 3.3.257.1
• Label: 3.3.257.1-9.2-b
• Conductor: 9.2
• Rank: \( 0 \)

Base field 3.3.257.1

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

Elliptic curves in class 9.2-b over 3.3.257.1

Isogeny class 9.2-b contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
9.2-b1	\( \bigl[a^{2} - 3\) , \( -a^{2} - a + 3\) , \( a^{2} - 3\) , \( -2 a^{2} + 14 a - 9\) , \( -18 a^{2} - 32 a + 31\bigr] \)
9.2-b2	\( \bigl[a^{2} - 3\) , \( -a^{2} - a + 3\) , \( a^{2} - 3\) , \( -2 a^{2} - 6 a + 6\) , \( -a^{2} - 5 a + 4\bigr] \)
9.2-b3	\( \bigl[a^{2} + a - 2\) , \( a^{2} + a - 4\) , \( 0\) , \( 4 a^{2} + 4 a - 12\) , \( 21 a^{2} + 28 a - 12\bigr] \)
9.2-b4	\( \bigl[a^{2} + a - 2\) , \( a^{2} + a - 4\) , \( 0\) , \( -a^{2} - a + 3\) , \( 0\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph