Elliptic curve isogeny class 71.4-d over number field 6.6.434581.1

• Base field: 6.6.434581.1
• Label: 6.6.434581.1-71.4-d
• Conductor: 71.4
• 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 71.4-d over 6.6.434581.1

Isogeny class 71.4-d contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
71.4-d1	\( \bigl[3 a^{5} - 6 a^{4} - 10 a^{3} + 12 a^{2} + 4 a - 2\) , \( a^{5} - 3 a^{4} - a^{3} + 6 a^{2} - a\) , \( 2 a^{5} - 5 a^{4} - 5 a^{3} + 12 a^{2} - 3\) , \( -5 a^{4} + 7 a^{3} + 20 a^{2} - 7 a - 5\) , \( -a^{5} - 4 a^{4} + 12 a^{3} + 19 a^{2} - 10 a - 6\bigr] \)
71.4-d2	\( \bigl[3 a^{5} - 6 a^{4} - 10 a^{3} + 12 a^{2} + 4 a - 2\) , \( a^{5} - 3 a^{4} - a^{3} + 6 a^{2} - a\) , \( 2 a^{5} - 5 a^{4} - 5 a^{3} + 12 a^{2} - 3\) , \( -25 a^{5} + 35 a^{4} + 122 a^{3} - 50 a^{2} - 142 a - 40\) , \( -120 a^{5} + 177 a^{4} + 588 a^{3} - 299 a^{2} - 700 a - 195\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph