Elliptic curve isogeny class 71.1-b over number field 6.6.434581.1

• Base field: 6.6.434581.1
• Label: 6.6.434581.1-71.1-b
• Conductor: 71.1
• Rank: \( 0 \)

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 71.1-b over 6.6.434581.1

Isogeny class 71.1-b contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
71.1-b1	\( \bigl[3 a^{5} - 6 a^{4} - 10 a^{3} + 12 a^{2} + 4 a - 2\) , \( -a^{5} + 6 a^{3} + 4 a^{2} - 5 a - 3\) , \( a^{5} - 2 a^{4} - 3 a^{3} + 4 a^{2} - 1\) , \( -297 a^{5} + 798 a^{4} + 604 a^{3} - 1840 a^{2} + 208 a + 366\) , \( -3433 a^{5} + 9442 a^{4} + 6587 a^{3} - 22010 a^{2} + 3003 a + 4476\bigr] \)
71.1-b2	\( \bigl[2 a^{5} - 4 a^{4} - 7 a^{3} + 8 a^{2} + 4 a - 1\) , \( -2 a^{4} + 3 a^{3} + 7 a^{2} - 3 a - 4\) , \( 3 a^{5} - 6 a^{4} - 10 a^{3} + 12 a^{2} + 5 a - 3\) , \( -3 a^{5} + 6 a^{4} + 9 a^{3} - 9 a^{2} - 3 a\) , \( -a^{5} + 2 a^{4} + 3 a^{3} - 4 a^{2} + a - 1\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph