Elliptic curve isogeny class 71.2-b over number field 6.6.300125.1

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

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

Curve label	Weierstrass Coefficients
71.2-b1	\( \bigl[-8 a^{5} + 2 a^{4} + 58 a^{3} + 27 a^{2} - 39 a - 12\) , \( 4 a^{5} - 2 a^{4} - 28 a^{3} - 7 a^{2} + 18 a + 1\) , \( -5 a^{5} + a^{4} + 37 a^{3} + 18 a^{2} - 26 a - 7\) , \( 22 a^{5} - 4 a^{4} - 160 a^{3} - 84 a^{2} + 102 a + 36\) , \( 12 a^{5} - 4 a^{4} - 87 a^{3} - 34 a^{2} + 62 a + 16\bigr] \)
71.2-b2	\( \bigl[-8 a^{5} + 2 a^{4} + 58 a^{3} + 27 a^{2} - 39 a - 12\) , \( 4 a^{5} - 2 a^{4} - 28 a^{3} - 7 a^{2} + 18 a + 1\) , \( -5 a^{5} + a^{4} + 37 a^{3} + 18 a^{2} - 26 a - 7\) , \( -8 a^{5} + 11 a^{4} + 45 a^{3} - 24 a^{2} - 8 a + 1\) , \( -10 a^{5} - 15 a^{4} + 96 a^{3} + 131 a^{2} - 97 a - 27\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph