Properties

Base field 5.5.36497.1
Label 5.5.36497.1-25.1-d
Conductor 25.1
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 25.1-d over 5.5.36497.1

Isogeny class 25.1-d contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
25.1-d1 \( \bigl[a^{2} - 2\) , \( a^{4} - 2 a^{3} - 4 a^{2} + 6 a + 3\) , \( a^{2} - 1\) , \( 3 a^{4} - 6 a^{3} - 10 a^{2} + 13 a + 6\) , \( -20 a^{4} + 12 a^{3} + 77 a^{2} + 9 a - 11\bigr] \)
25.1-d2 \( \bigl[2 a^{4} - 3 a^{3} - 7 a^{2} + 7 a + 3\) , \( -a^{2} + 1\) , \( a^{4} - 2 a^{3} - 2 a^{2} + 5 a - 1\) , \( -8 a^{4} - 21 a^{3} + 15 a^{2} + 40 a - 7\) , \( -51 a^{4} - 10 a^{3} + 111 a^{2} - a - 9\bigr] \)
25.1-d3 \( \bigl[a^{4} - a^{3} - 3 a^{2} + 2 a\) , \( -a^{4} + 2 a^{3} + 2 a^{2} - 3 a + 1\) , \( a^{2} - 2\) , \( 89 a^{4} - 17 a^{3} - 439 a^{2} - 38 a + 86\) , \( -819 a^{4} + 586 a^{3} + 3095 a^{2} + 134 a - 596\bigr] \)
25.1-d4 \( \bigl[a^{2} - 2\) , \( a^{4} - 2 a^{3} - 4 a^{2} + 6 a + 3\) , \( a^{2} - 1\) , \( 143 a^{4} - 101 a^{3} - 555 a^{2} + 8 a + 86\) , \( 747 a^{4} - 457 a^{3} - 2953 a^{2} - 247 a + 559\bigr] \)

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