Properties

Base field 5.5.65657.1
Label 5.5.65657.1-15.1-a
Conductor 15.1
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 15.1-a over 5.5.65657.1

Isogeny class 15.1-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
15.1-a1 \( \bigl[-2 a^{4} + 3 a^{3} + 9 a^{2} - 9 a - 6\) , \( -2 a^{4} + 3 a^{3} + 8 a^{2} - 7 a - 5\) , \( -a^{4} + a^{3} + 5 a^{2} - 2 a - 4\) , \( -46 a^{4} + 109 a^{3} + 43 a^{2} - 117 a - 48\) , \( 463 a^{4} - 1139 a^{3} - 594 a^{2} + 1290 a + 662\bigr] \)
15.1-a2 \( \bigl[a^{2} - 2\) , \( a^{4} - a^{3} - 4 a^{2} + 2 a + 2\) , \( a^{2} - 2\) , \( 10 a^{4} - 10 a^{3} - 40 a^{2} + 16 a + 5\) , \( -25 a^{4} + 18 a^{3} + 100 a^{2} - 13 a - 9\bigr] \)
15.1-a3 \( \bigl[a^{2} - 2\) , \( a^{4} - a^{3} - 4 a^{2} + 2 a + 2\) , \( a^{2} - 2\) , \( a\) , \( -a^{4} + a^{3} + 4 a^{2} - a - 1\bigr] \)
15.1-a4 \( \bigl[a^{2} - 2\) , \( a^{4} - a^{3} - 4 a^{2} + 2 a + 2\) , \( a^{2} - 2\) , \( 20 a^{4} - 20 a^{3} - 75 a^{2} + 26 a\) , \( 30 a^{4} - 29 a^{3} - 120 a^{2} + 39 a + 19\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph