Elliptic curve isogeny class 47.1-c over number field 6.6.1541581.1

• Base field: 6.6.1541581.1
• Label: 6.6.1541581.1-47.1-c
• Conductor: 47.1
• Rank: \( 0 \)

Base field 6.6.1541581.1

Generator \(a\), with minimal polynomial \( x^{6} - x^{5} - 6 x^{4} + 2 x^{3} + 9 x^{2} + x - 1 \); class number \(1\).

Elliptic curves in class 47.1-c over 6.6.1541581.1

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

Curve label	Weierstrass Coefficients
47.1-c1	\( \bigl[a^{5} - 2 a^{4} - 4 a^{3} + 5 a^{2} + 5 a\) , \( -a^{4} + 2 a^{3} + 3 a^{2} - 5 a - 1\) , \( 2 a^{5} - 3 a^{4} - 10 a^{3} + 8 a^{2} + 13 a - 1\) , \( 5 a^{4} + 3 a^{3} - 28 a^{2} - 28 a + 6\) , \( 13 a^{5} + 10 a^{4} - 66 a^{3} - 94 a^{2} - 16 a + 13\bigr] \)
47.1-c2	\( \bigl[a + 1\) , \( a^{5} - a^{4} - 7 a^{3} + 4 a^{2} + 10 a\) , \( 2 a^{5} - 4 a^{4} - 7 a^{3} + 10 a^{2} + 5 a - 1\) , \( 74 a^{5} - 113 a^{4} - 381 a^{3} + 327 a^{2} + 502 a - 156\) , \( -97 a^{5} + 88 a^{4} + 683 a^{3} - 403 a^{2} - 971 a + 290\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph