Elliptic curve isogeny class 47.1-b over number field 6.6.1081856.1

• Base field: 6.6.1081856.1
• Label: 6.6.1081856.1-47.1-b
• Conductor: 47.1
• Rank: \( 1 \)

Base field 6.6.1081856.1

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

Elliptic curves in class 47.1-b over 6.6.1081856.1

Isogeny class 47.1-b contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
47.1-b1	\( \bigl[a^{5} - 6 a^{3} - a^{2} + 7 a\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 6 a + 1\) , \( a^{4} - a^{3} - 4 a^{2} + 2 a + 3\) , \( 43 a^{5} + 13 a^{4} - 250 a^{3} - 162 a^{2} + 238 a + 149\) , \( 1481 a^{5} + 402 a^{4} - 8776 a^{3} - 5351 a^{2} + 8915 a + 5407\bigr] \)
47.1-b2	\( \bigl[a^{4} - 5 a^{2} + 3\) , \( a^{5} - 2 a^{4} - 5 a^{3} + 7 a^{2} + 5 a - 2\) , \( a^{5} - a^{4} - 5 a^{3} + 2 a^{2} + 5 a + 1\) , \( 2 a^{5} - 6 a^{4} - 8 a^{3} + 21 a^{2} + 4 a - 5\) , \( 2 a^{5} + 3 a^{4} - 2 a^{3} - a^{2} - a - 1\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph