Elliptic curve isogeny class 55.2-b over number field 3.3.985.1

• Base field: 3.3.985.1
• Label: 3.3.985.1-55.2-b
• Conductor: 55.2
• Rank: \( 0 \)

Base field 3.3.985.1

Generator \(a\), with minimal polynomial \( x^{3} - x^{2} - 6 x + 1 \); class number \(1\).

Elliptic curves in class 55.2-b over 3.3.985.1

Isogeny class 55.2-b contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
55.2-b1	\( \bigl[a^{2} - 4\) , \( -a^{2} + 4\) , \( 1\) , \( -6 a^{2} + 159 a - 417\) , \( -807 a^{2} + 1713 a + 1911\bigr] \)
55.2-b2	\( \bigl[a^{2} - 4\) , \( -a^{2} + 4\) , \( 1\) , \( -61 a^{2} + 189 a - 32\) , \( -615 a^{2} + 1902 a - 292\bigr] \)
55.2-b3	\( \bigl[a^{2} - 4\) , \( -a^{2} + 4\) , \( 1\) , \( -31 a^{2} + 89 a + 3\) , \( 196 a^{2} - 608 a + 98\bigr] \)
55.2-b4	\( \bigl[a^{2} - 4\) , \( -a^{2} + 4\) , \( 1\) , \( -6 a^{2} + 9 a + 23\) , \( -a^{2} - 5 a + 23\bigr] \)

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