Elliptic curve isogeny class 31.1-b over number field 6.6.485125.1

• Base field: 6.6.485125.1
• Label: 6.6.485125.1-31.1-b
• Conductor: 31.1
• Rank: \( 1 \)

Base field 6.6.485125.1

Generator \(a\), with minimal polynomial \( x^{6} - 2 x^{5} - 4 x^{4} + 8 x^{3} + 2 x^{2} - 5 x + 1 \); class number \(1\).

Elliptic curves in class 31.1-b over 6.6.485125.1

Isogeny class 31.1-b contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
31.1-b1	\( \bigl[a^{5} - 5 a^{3} + 4 a + 1\) , \( 3 a^{5} - 4 a^{4} - 13 a^{3} + 13 a^{2} + 11 a - 4\) , \( -a^{5} + 2 a^{4} + 5 a^{3} - 7 a^{2} - 6 a + 3\) , \( -4 a^{5} - 11 a^{4} + 30 a^{3} + 30 a^{2} - 7 a - 3\) , \( 11 a^{5} + 22 a^{4} - 105 a^{3} - 11 a^{2} + 75 a - 16\bigr] \)
31.1-b2	\( \bigl[a^{5} - 5 a^{3} + 4 a + 1\) , \( 3 a^{5} - 4 a^{4} - 13 a^{3} + 13 a^{2} + 11 a - 4\) , \( -a^{5} + 2 a^{4} + 5 a^{3} - 7 a^{2} - 6 a + 3\) , \( 11 a^{5} - 11 a^{4} - 50 a^{3} + 35 a^{2} + 43 a - 13\) , \( 5 a^{5} - 4 a^{4} - 24 a^{3} + 15 a^{2} + 21 a - 6\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph