Elliptic curve isogeny class 55.2-a over number field 3.3.985.1

• Base field: 3.3.985.1
• Label: 3.3.985.1-55.2-a
• Conductor: 55.2
• Rank: \( 1 \)

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-a over 3.3.985.1

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

Curve label	Weierstrass Coefficients
55.2-a1	\( \bigl[a^{2} - a - 4\) , \( 0\) , \( a^{2} - a - 4\) , \( 309 a^{2} - 259 a - 1906\) , \( 5697 a^{2} - 4767 a - 34965\bigr] \)
55.2-a2	\( \bigl[a^{2} - a - 4\) , \( 0\) , \( a^{2} - a - 4\) , \( 19 a^{2} - 14 a - 121\) , \( 110 a^{2} - 90 a - 681\bigr] \)
55.2-a3	\( \bigl[a^{2} - a - 4\) , \( 0\) , \( a^{2} - a - 4\) , \( 4 a^{2} - 4 a - 31\) , \( 11 a^{2} - 8 a - 66\bigr] \)
55.2-a4	\( \bigl[a^{2} - a - 4\) , \( 0\) , \( a^{2} - a - 4\) , \( -a^{2} + a + 4\) , \( -a^{2} + a + 5\bigr] \)

Rank

Rank: \( 1 \)

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