Elliptic curve isogeny class 71.3-b over number field 6.6.300125.1

• Base field: 6.6.300125.1
• Label: 6.6.300125.1-71.3-b
• Conductor: 71.3
• 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 71.3-b over 6.6.300125.1

Isogeny class 71.3-b contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
71.3-b1	\( \bigl[-6 a^{5} + a^{4} + 44 a^{3} + 23 a^{2} - 28 a - 10\) , \( 3 a^{5} - a^{4} - 21 a^{3} - 8 a^{2} + 12 a + 3\) , \( -5 a^{5} + a^{4} + 37 a^{3} + 18 a^{2} - 26 a - 7\) , \( -82 a^{5} + 24 a^{4} + 591 a^{3} + 257 a^{2} - 391 a - 116\) , \( 161 a^{5} - 45 a^{4} - 1160 a^{3} - 509 a^{2} + 769 a + 227\bigr] \)
71.3-b2	\( \bigl[-5 a^{5} + a^{4} + 37 a^{3} + 18 a^{2} - 26 a - 7\) , \( 3 a^{5} - a^{4} - 21 a^{3} - 9 a^{2} + 13 a + 3\) , \( 3 a^{5} - a^{4} - 21 a^{3} - 9 a^{2} + 13 a + 4\) , \( 13 a^{5} - 3 a^{4} - 93 a^{3} - 43 a^{2} + 59 a + 17\) , \( -7 a^{5} + 2 a^{4} + 52 a^{3} + 25 a^{2} - 31 a - 9\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph