Properties

Base field 5.5.160801.1
Label 5.5.160801.1-9.3-b
Conductor 9.3
Rank \( 1 \)

Related objects

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Base field 5.5.160801.1

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

Elliptic curves in class 9.3-b over 5.5.160801.1

Isogeny class 9.3-b contains 2 curves linked by isogenies of degree 3.

Curve label Weierstrass Coefficients
9.3-b1 \( \bigl[a^{4} - a^{3} - 5 a^{2} + 5 a + 3\) , \( a^{2} + a - 1\) , \( 2 a^{4} - a^{3} - 9 a^{2} + 5 a + 2\) , \( -a^{3} + 2 a^{2} + 8 a - 4\) , \( 3 a^{4} - 2 a^{3} - 12 a^{2} + 9 a - 2\bigr] \)
9.3-b2 \( \bigl[2 a^{4} - a^{3} - 9 a^{2} + 5 a + 3\) , \( a^{4} - 6 a^{2} + a + 5\) , \( a^{4} - 5 a^{2} + 3\) , \( 2 a^{4} + 5 a^{3} - 5 a^{2} - 13 a + 6\) , \( 7 a^{4} + 4 a^{3} - 26 a^{2} - 2 a + 16\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph