Properties

Base field 5.5.65657.1
Label 5.5.65657.1-225.1-a
Conductor 225.1
Rank not recorded

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Base field 5.5.65657.1

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

Elliptic curves in class 225.1-a over 5.5.65657.1

Isogeny class 225.1-a contains 4 curves linked by isogenies of degrees dividing 15.

Curve label Weierstrass Coefficients
225.1-a1 \( \bigl[-2 a^{4} + 3 a^{3} + 9 a^{2} - 8 a - 7\) , \( -2 a^{4} + 2 a^{3} + 9 a^{2} - 6 a - 7\) , \( a^{4} - a^{3} - 4 a^{2} + 2 a + 2\) , \( 1196 a^{4} - 2255 a^{3} - 4356 a^{2} + 5795 a + 970\) , \( -39450 a^{4} + 69900 a^{3} + 153230 a^{2} - 182868 a - 68777\bigr] \)
225.1-a2 \( \bigl[a^{3} - 3 a - 1\) , \( -a^{3} + 5 a + 2\) , \( -a^{4} + a^{3} + 5 a^{2} - 2 a - 4\) , \( -5 a^{4} + 304 a^{3} - 129 a^{2} - 1151 a - 408\) , \( -3090 a^{4} + 1758 a^{3} + 12427 a^{2} + 1570 a - 1030\bigr] \)
225.1-a3 \( \bigl[a^{2} - a - 2\) , \( -a^{4} + a^{3} + 5 a^{2} - 3 a - 3\) , \( -2 a^{4} + 3 a^{3} + 9 a^{2} - 9 a - 6\) , \( 51 a^{4} + 19 a^{3} - 225 a^{2} - 219 a - 42\) , \( -427 a^{4} - 168 a^{3} + 1923 a^{2} + 1797 a + 312\bigr] \)
225.1-a4 \( \bigl[-a^{4} + 2 a^{3} + 5 a^{2} - 7 a - 4\) , \( a^{3} - a^{2} - 4 a\) , \( -2 a^{4} + 3 a^{3} + 9 a^{2} - 9 a - 6\) , \( 3 a^{4} - 5 a^{3} - 12 a^{2} + 16 a + 2\) , \( 9 a^{4} - 20 a^{3} - 32 a^{2} + 65 a + 14\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 5 & 15 \\ 3 & 1 & 15 & 5 \\ 5 & 15 & 1 & 3 \\ 15 & 5 & 3 & 1 \end{array}\right)\)

Isogeny graph