Properties

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

Related objects

Learn more about

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-a over 5.5.36497.1

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

Curve label Weierstrass Coefficients
9.1-a1 \( \bigl[a^{4} - 2 a^{3} - 3 a^{2} + 6 a + 1\) , \( a^{4} - a^{3} - 4 a^{2} + a + 2\) , \( a^{4} - a^{3} - 4 a^{2} + 2 a + 3\) , \( 106 a^{4} - 70 a^{3} - 413 a^{2} - 23 a + 81\) , \( 2837 a^{4} - 1889 a^{3} - 11031 a^{2} - 533 a + 2126\bigr] \)
9.1-a2 \( \bigl[a\) , \( -a^{3} + 5 a\) , \( a^{4} - a^{3} - 4 a^{2} + 2 a + 3\) , \( 76 a^{4} - 83 a^{3} - 258 a^{2} + 73 a - 19\) , \( -302 a^{4} + 116 a^{3} + 1335 a^{2} + 348 a - 480\bigr] \)
9.1-a3 \( \bigl[a^{2} - a - 2\) , \( a^{3} - a^{2} - 4 a + 1\) , \( a^{2} - a - 2\) , \( -a^{4} - 2 a^{3} + 6 a^{2} + 8 a - 11\) , \( 36 a^{4} - 88 a^{3} - 60 a^{2} + 206 a - 75\bigr] \)
9.1-a4 \( \bigl[2 a^{4} - 3 a^{3} - 7 a^{2} + 8 a + 3\) , \( a^{2} - a - 3\) , \( a^{4} - a^{3} - 4 a^{2} + 3 a + 3\) , \( 71 a^{4} - 36 a^{3} - 299 a^{2} - 24 a + 56\) , \( 497 a^{4} - 316 a^{3} - 1964 a^{2} - 104 a + 377\bigr] \)

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