Elliptic Curve Isogeny Class 71.1-b over Number Field 6.6.300125.1

• Base field: 6.6.300125.1
• Label: 6.6.300125.1-71.1-b
• Conductor: 71.1
• Rank: not recorded

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 71.1-b over 6.6.300125.1

Isogeny class 71.1-b contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
71.1-b1	\( \bigl[a^{5} - 7 a^{3} - 5 a^{2} + 3 a + 2\) , \( -3 a^{5} + a^{4} + 21 a^{3} + 9 a^{2} - 11 a - 5\) , \( -2 a^{5} + 15 a^{3} + 10 a^{2} - 9 a - 5\) , \( 78 a^{5} - 17 a^{4} - 560 a^{3} - 282 a^{2} + 331 a + 105\) , \( -183 a^{5} + 43 a^{4} + 1314 a^{3} + 637 a^{2} - 791 a - 228\bigr] \)
71.1-b2	\( \bigl[-4 a^{5} + a^{4} + 29 a^{3} + 14 a^{2} - 20 a - 6\) , \( -a^{5} - a^{4} + 9 a^{3} + 10 a^{2} - 8 a - 4\) , \( -3 a^{5} + 23 a^{3} + 14 a^{2} - 17 a - 6\) , \( -8 a^{5} + a^{4} + 59 a^{3} + 33 a^{2} - 42 a - 13\) , \( -3 a^{5} + 23 a^{3} + 14 a^{2} - 17 a - 5\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

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

Isogeny graph