Properties

Base field 5.5.36497.1
Label 5.5.36497.1-25.1-a
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-a over 5.5.36497.1

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

Curve label Weierstrass Coefficients
25.1-a1 \( \bigl[2 a^{4} - 3 a^{3} - 6 a^{2} + 7 a + 1\) , \( -2 a^{4} + 3 a^{3} + 8 a^{2} - 7 a - 5\) , \( a^{4} - 2 a^{3} - 2 a^{2} + 4 a - 1\) , \( 2 a^{4} - 2 a^{3} - 4 a^{2} + 4 a\) , \( 2 a^{4} - a^{3} - 5 a^{2} + 2 a\bigr] \)
25.1-a2 \( \bigl[a^{4} - 2 a^{3} - 3 a^{2} + 5 a + 2\) , \( a^{4} - a^{3} - 5 a^{2} + 4 a + 4\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 6 a + 2\) , \( 20 a^{4} - 18 a^{3} - 76 a^{2} + 10 a + 20\) , \( 69 a^{4} - 48 a^{3} - 268 a^{2} - 6 a + 54\bigr] \)
25.1-a3 \( \bigl[a^{4} - 2 a^{3} - 3 a^{2} + 6 a + 1\) , \( -a^{4} + 2 a^{3} + 4 a^{2} - 5 a - 4\) , \( a^{4} - a^{3} - 4 a^{2} + 3 a + 2\) , \( -5 a^{4} - 14 a^{3} - 11 a^{2} + 55 a - 20\) , \( -63 a^{4} - 115 a^{3} + 166 a^{2} + 193 a - 100\bigr] \)
25.1-a4 \( \bigl[a^{4} - a^{3} - 3 a^{2} + 2 a + 1\) , \( -a^{4} + 2 a^{3} + 3 a^{2} - 4 a - 2\) , \( a^{2} - 1\) , \( -53 a^{4} + 93 a^{3} + 155 a^{2} - 135 a - 149\) , \( -157 a^{4} + 112 a^{3} + 991 a^{2} - 666 a - 644\bigr] \)

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