Elliptic curve isogeny class 71.2-a over number field 6.6.300125.1

• Base field: 6.6.300125.1
• Label: 6.6.300125.1-71.2-a
• Conductor: 71.2
• 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 71.2-a over 6.6.300125.1

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

Curve label	Weierstrass Coefficients
71.2-a1	\( \bigl[-8 a^{5} + 2 a^{4} + 58 a^{3} + 27 a^{2} - 38 a - 12\) , \( 4 a^{5} - a^{4} - 29 a^{3} - 13 a^{2} + 18 a + 6\) , \( -4 a^{5} + a^{4} + 29 a^{3} + 14 a^{2} - 19 a - 7\) , \( 41 a^{5} - 12 a^{4} - 293 a^{3} - 130 a^{2} + 184 a + 51\) , \( 48 a^{5} - 13 a^{4} - 345 a^{3} - 156 a^{2} + 217 a + 61\bigr] \)
71.2-a2	\( \bigl[-a^{5} + 8 a^{3} + 5 a^{2} - 8 a - 2\) , \( -3 a^{5} + a^{4} + 21 a^{3} + 8 a^{2} - 10 a - 2\) , \( -3 a^{5} + 23 a^{3} + 14 a^{2} - 17 a - 6\) , \( -20 a^{5} + 4 a^{4} + 141 a^{3} + 70 a^{2} - 82 a - 32\) , \( 14 a^{5} - 46 a^{4} - 93 a^{3} + 229 a^{2} + 129 a - 177\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph