Properties

Base field 6.6.592661.1
Label 6.6.592661.1-31.1-b
Conductor 31.1
Rank \( 0 \)

Related objects

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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-b over 6.6.592661.1

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

Curve label Weierstrass Coefficients
31.1-b1 \( \bigl[2 a^{5} - a^{4} - 9 a^{3} + 5 a^{2} + 6 a - 5\) , \( 2 a^{5} - 3 a^{4} - 9 a^{3} + 12 a^{2} + 6 a - 4\) , \( a^{4} - 4 a^{2} + 1\) , \( -a^{5} + 7 a^{3} - a^{2} - 5 a + 4\) , \( 4 a^{5} - 4 a^{4} - 18 a^{3} + 19 a^{2} + 12 a - 10\bigr] \)
31.1-b2 \( \bigl[a^{5} - a^{4} - 5 a^{3} + 5 a^{2} + 4 a - 4\) , \( -a^{5} + 2 a^{4} + 5 a^{3} - 9 a^{2} - 5 a + 6\) , \( a^{5} - 4 a^{3} + a - 1\) , \( -18 a^{5} + 35 a^{4} + 48 a^{3} - 86 a^{2} - 25 a + 31\) , \( -51 a^{5} + 152 a^{4} - 32 a^{3} - 169 a^{2} + 64 a + 14\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph