Elliptic curve isogeny class 31.1-a over number field 6.6.592661.1

• Base field: 6.6.592661.1
• Label: 6.6.592661.1-31.1-a
• Conductor: 31.1
• Rank: \( 0 \)

Base field 6.6.592661.1

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

Elliptic curves in class 31.1-a over 6.6.592661.1

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

Curve label	Weierstrass Coefficients
31.1-a1	\( \bigl[a^{5} - 5 a^{3} + a^{2} + 4 a - 2\) , \( a^{5} - 5 a^{3} + a^{2} + 3 a - 3\) , \( a^{5} - a^{4} - 5 a^{3} + 5 a^{2} + 4 a - 3\) , \( 17 a^{5} - 24 a^{4} - 67 a^{3} + 89 a^{2} + 21 a - 30\) , \( -32 a^{5} + 64 a^{4} + 107 a^{3} - 253 a^{2} + 71 a + 24\bigr] \)
31.1-a2	\( \bigl[2 a^{5} - a^{4} - 9 a^{3} + 4 a^{2} + 5 a - 2\) , \( 2 a^{5} - 3 a^{4} - 9 a^{3} + 13 a^{2} + 6 a - 7\) , \( a^{5} - 4 a^{3} + 2 a - 1\) , \( -3 a^{5} - a^{4} + 20 a^{3} - 5 a^{2} - 15 a + 3\) , \( -3 a^{5} + 5 a^{4} + a^{3} + 3 a^{2} - 6\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph