Elliptic curve isogeny class 71.6-b over number field 6.6.300125.1

• Base field: 6.6.300125.1
• Label: 6.6.300125.1-71.6-b
• Conductor: 71.6
• Rank: \( 1 \)

Base field 6.6.300125.1

Generator \(a\), with minimal polynomial \( x^{6} - x^{5} - 7 x^{4} + 2 x^{3} + 7 x^{2} - 2 x - 1 \); class number \(1\).

Elliptic curves in class 71.6-b over 6.6.300125.1

Isogeny class 71.6-b contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
71.6-b1	\( \bigl[-3 a^{5} + a^{4} + 22 a^{3} + 8 a^{2} - 17 a - 3\) , \( a^{5} - a^{4} - 6 a^{3} + a^{2} + a - 2\) , \( -6 a^{5} + a^{4} + 44 a^{3} + 23 a^{2} - 29 a - 10\) , \( -14 a^{5} + 3 a^{4} + 102 a^{3} + 49 a^{2} - 67 a - 19\) , \( -4 a^{5} + a^{4} + 29 a^{3} + 14 a^{2} - 20 a - 6\bigr] \)
71.6-b2	\( \bigl[-3 a^{5} + a^{4} + 22 a^{3} + 8 a^{2} - 17 a - 3\) , \( a^{5} - a^{4} - 6 a^{3} + a^{2} + a - 2\) , \( -6 a^{5} + a^{4} + 44 a^{3} + 23 a^{2} - 29 a - 10\) , \( -19 a^{5} + 3 a^{4} + 137 a^{3} + 74 a^{2} - 87 a - 34\) , \( a^{5} + 4 a^{4} - 7 a^{3} - 23 a^{2} + 15\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph