Elliptic curve isogeny class 71.5-a over number field 6.6.300125.1

• Base field: 6.6.300125.1
• Label: 6.6.300125.1-71.5-a
• Conductor: 71.5
• 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 71.5-a over 6.6.300125.1

Isogeny class 71.5-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
71.5-a1	\( \bigl[-6 a^{5} + 2 a^{4} + 43 a^{3} + 17 a^{2} - 29 a - 7\) , \( a^{5} - 8 a^{3} - 4 a^{2} + 7 a + 2\) , \( -6 a^{5} + a^{4} + 44 a^{3} + 23 a^{2} - 28 a - 10\) , \( 108 a^{5} - 25 a^{4} - 776 a^{3} - 378 a^{2} + 466 a + 140\) , \( 536 a^{5} - 123 a^{4} - 3847 a^{3} - 1892 a^{2} + 2295 a + 696\bigr] \)
71.5-a2	\( \bigl[-8 a^{5} + 2 a^{4} + 58 a^{3} + 27 a^{2} - 38 a - 12\) , \( -6 a^{5} + 2 a^{4} + 43 a^{3} + 17 a^{2} - 30 a - 6\) , \( -3 a^{5} + 23 a^{3} + 14 a^{2} - 17 a - 6\) , \( 10 a^{5} - 2 a^{4} - 72 a^{3} - 41 a^{2} + 36 a + 12\) , \( 15 a^{5} - 27 a^{4} - 174 a^{3} - 76 a^{2} + 101 a + 30\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph