Elliptic curve isogeny class 49.1-b over number field 6.6.434581.1

• Base field: 6.6.434581.1
• Label: 6.6.434581.1-49.1-b
• Conductor: 49.1
• Rank: \( 1 \)

Base field 6.6.434581.1

Generator \(a\), with minimal polynomial \( x^{6} - 2 x^{5} - 4 x^{4} + 5 x^{3} + 4 x^{2} - 2 x - 1 \); class number \(1\).

Elliptic curves in class 49.1-b over 6.6.434581.1

Isogeny class 49.1-b contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
49.1-b1	\( \bigl[2 a^{5} - 4 a^{4} - 6 a^{3} + 7 a^{2} + 2 a - 1\) , \( 2 a^{5} - 5 a^{4} - 5 a^{3} + 11 a^{2} + a - 3\) , \( a^{5} - a^{4} - 5 a^{3} + 4 a + 2\) , \( -a^{5} + a^{4} + 7 a^{3} - 3 a^{2} - 11 a + 1\) , \( 2 a^{5} - 5 a^{4} - 5 a^{3} + 12 a^{2} - 4\bigr] \)
49.1-b2	\( \bigl[a^{5} - a^{4} - 5 a^{3} + 5 a + 1\) , \( 2 a^{5} - 3 a^{4} - 8 a^{3} + 4 a^{2} + 5 a - 1\) , \( a^{5} - 2 a^{4} - 3 a^{3} + 4 a^{2}\) , \( 3 a^{5} - 8 a^{4} - 8 a^{3} + 21 a^{2} + 5 a - 7\) , \( -5 a^{5} + 13 a^{4} + 14 a^{3} - 36 a^{2} - 6 a + 15\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph