Elliptic curve isogeny class 71.6-a over number field 6.6.300125.1

• Base field: 6.6.300125.1
• Label: 6.6.300125.1-71.6-a
• Conductor: 71.6
• Rank: \( 0 \)

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-a over 6.6.300125.1

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

Curve label	Weierstrass Coefficients
71.6-a1	\( \bigl[-2 a^{5} + a^{4} + 14 a^{3} + 4 a^{2} - 10 a - 2\) , \( -3 a^{5} + 2 a^{4} + 20 a^{3} + 3 a^{2} - 13 a - 1\) , \( a^{5} - a^{4} - 6 a^{3} + a^{2} + 3 a\) , \( -a^{5} + 20 a^{4} - 20 a^{3} - 104 a^{2} + 46 a + 16\) , \( -403 a^{5} + 171 a^{4} + 2816 a^{3} + 961 a^{2} - 1694 a - 488\bigr] \)
71.6-a2	\( \bigl[-4 a^{5} + a^{4} + 29 a^{3} + 13 a^{2} - 19 a - 5\) , \( -a^{2} + a + 3\) , \( -6 a^{5} + a^{4} + 44 a^{3} + 23 a^{2} - 29 a - 10\) , \( -42 a^{5} + 38 a^{4} + 266 a^{3} - 15 a^{2} - 116 a - 22\) , \( -177 a^{5} + 241 a^{4} + 1008 a^{3} - 518 a^{2} - 238 a - 6\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph