Properties

Base field 5.5.70601.1
Label 5.5.70601.1-47.1-a
Conductor 47.1
Rank \( 0 \)

Related objects

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Base field 5.5.70601.1

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

Elliptic curves in class 47.1-a over 5.5.70601.1

Isogeny class 47.1-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label Weierstrass Coefficients
47.1-a1 \( \bigl[2 a^{4} - a^{3} - 10 a^{2} + 3\) , \( a^{3} - a^{2} - 3 a + 1\) , \( 2 a^{4} - 2 a^{3} - 9 a^{2} + 4 a + 2\) , \( -3 a^{4} + 8 a^{3} + 3 a^{2} - 7 a - 2\) , \( -6 a^{4} + 17 a^{3} - 10 a\bigr] \)
47.1-a2 \( \bigl[2 a^{4} - 2 a^{3} - 9 a^{2} + 3 a + 3\) , \( a^{4} - 6 a^{2} - a + 3\) , \( a^{4} - 6 a^{2} - 2 a + 4\) , \( 47 a^{4} - 31 a^{3} - 246 a^{2} + 10 a + 150\) , \( -159 a^{4} + 108 a^{3} + 829 a^{2} - 51 a - 493\bigr] \)
47.1-a3 \( \bigl[a\) , \( a^{4} - 7 a^{2} - a + 5\) , \( 0\) , \( -24 a^{4} + 12 a^{3} + 136 a^{2} - 4 a - 84\) , \( -115 a^{4} + 96 a^{3} + 555 a^{2} - 49 a - 327\bigr] \)
47.1-a4 \( \bigl[2 a^{4} - a^{3} - 10 a^{2} + 3\) , \( a^{3} - a^{2} - 3 a + 1\) , \( 2 a^{4} - 2 a^{3} - 9 a^{2} + 4 a + 2\) , \( -3 a^{4} + 8 a^{3} + 8 a^{2} - 12 a - 27\) , \( -6 a^{4} + 18 a^{3} + 12 a^{2} - 25 a - 60\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph