Elliptic curve isogeny class 55.1-b over number field 6.6.1241125.1

• Base field: 6.6.1241125.1
• Label: 6.6.1241125.1-55.1-b
• Conductor: 55.1
• Rank: \( 1 \)

Base field 6.6.1241125.1

Generator \(a\), with minimal polynomial \( x^{6} - 7 x^{4} - 2 x^{3} + 11 x^{2} + 7 x + 1 \); class number \(1\).

Elliptic curves in class 55.1-b over 6.6.1241125.1

Isogeny class 55.1-b contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
55.1-b1	\( \bigl[-2 a^{5} + a^{4} + 13 a^{3} - 2 a^{2} - 19 a - 5\) , \( 4 a^{5} - a^{4} - 27 a^{3} - a^{2} + 42 a + 16\) , \( -3 a^{5} + 2 a^{4} + 20 a^{3} - 5 a^{2} - 31 a - 10\) , \( 9 a^{5} - 10 a^{4} - 43 a^{3} + 8 a^{2} + 72 a + 26\) , \( -37 a^{5} + 75 a^{4} + 112 a^{3} - 157 a^{2} - 114 a - 13\bigr] \)
55.1-b2	\( \bigl[-5 a^{5} + 2 a^{4} + 34 a^{3} - 2 a^{2} - 53 a - 19\) , \( a^{5} - 6 a^{3} - 2 a^{2} + 7 a + 4\) , \( -3 a^{5} + 2 a^{4} + 20 a^{3} - 5 a^{2} - 31 a - 10\) , \( 40 a^{5} - 9 a^{4} - 279 a^{3} - 20 a^{2} + 451 a + 188\) , \( 92 a^{5} - 18 a^{4} - 641 a^{3} - 53 a^{2} + 1023 a + 424\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph