Elliptic curve isogeny class 71.2-d over number field 6.6.434581.1

• Base field: 6.6.434581.1
• Label: 6.6.434581.1-71.2-d
• Conductor: 71.2
• 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 71.2-d over 6.6.434581.1

Isogeny class 71.2-d contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
71.2-d1	\( \bigl[2 a^{5} - 3 a^{4} - 8 a^{3} + 4 a^{2} + 4 a\) , \( -2 a^{5} + 6 a^{4} + 3 a^{3} - 15 a^{2} + 4 a + 5\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 3 a + 2\) , \( -3 a^{5} - 7 a^{4} + 28 a^{3} + 38 a^{2} - 19 a - 10\) , \( -16 a^{5} + 19 a^{4} + 67 a^{3} - 8 a^{2} - 22 a - 4\bigr] \)
71.2-d2	\( \bigl[a^{5} - 2 a^{4} - 3 a^{3} + 4 a^{2}\) , \( -a^{5} + a^{4} + 5 a^{3} - a^{2} - 2 a + 1\) , \( a^{5} - 2 a^{4} - 3 a^{3} + 3 a^{2} + 2 a\) , \( 124 a^{5} - 300 a^{4} - 372 a^{3} + 773 a^{2} + 203 a - 328\) , \( 871 a^{5} - 2082 a^{4} - 2669 a^{3} + 5381 a^{2} + 1425 a - 2290\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph