Properties

Base field 5.5.36497.1
Label 5.5.36497.1-9.1-b
Conductor 9.1
Rank not recorded

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Base field 5.5.36497.1

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

Elliptic curves in class 9.1-b over 5.5.36497.1

Isogeny class 9.1-b contains 4 curves linked by isogenies of degrees dividing 6.

Curve label Weierstrass Coefficients
9.1-b1 \( \bigl[a + 1\) , \( a^{4} - a^{3} - 3 a^{2} + a - 1\) , \( 0\) , \( 2 a^{2} - a\) , \( 0\bigr] \)
9.1-b2 \( \bigl[a^{4} - a^{3} - 4 a^{2} + 3 a + 2\) , \( 2 a^{4} - 3 a^{3} - 7 a^{2} + 7 a + 3\) , \( a^{4} - a^{3} - 4 a^{2} + 2 a + 2\) , \( 9 a^{4} + 38 a^{3} - 125 a^{2} - 29 a + 5\) , \( -52 a^{4} + 394 a^{3} - 503 a^{2} - 335 a + 53\bigr] \)
9.1-b3 \( \bigl[a^{4} - a^{3} - 4 a^{2} + 3 a + 2\) , \( 2 a^{4} - 3 a^{3} - 7 a^{2} + 7 a + 3\) , \( a^{4} - a^{3} - 4 a^{2} + 2 a + 2\) , \( -11 a^{4} + 18 a^{3} + 35 a^{2} - 29 a - 20\) , \( -37 a^{4} + 72 a^{3} + 122 a^{2} - 163 a - 101\bigr] \)
9.1-b4 \( \bigl[a + 1\) , \( a^{4} - a^{3} - 3 a^{2} + a - 1\) , \( 0\) , \( -8 a^{2} + 4 a\) , \( -14 a^{4} + 5 a^{3} + 40 a^{2} - 7 a - 4\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

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

Isogeny graph