Properties

Base field 4.4.4205.1
Label 4.4.4205.1-25.2-a
Conductor 25.2
Rank \( 0 \)

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Base field 4.4.4205.1

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

Elliptic curves in class 25.2-a over 4.4.4205.1

Isogeny class 25.2-a contains 4 curves linked by isogenies of degrees dividing 10.

Curve label Weierstrass Coefficients
25.2-a1 \( \bigl[a^{3} - a^{2} - 5 a\) , \( a^{3} - 2 a^{2} - 4 a + 2\) , \( -a^{3} + 2 a^{2} + 4 a\) , \( -9 a^{3} - 33 a^{2} - 21 a + 7\) , \( -91 a^{3} - 175 a^{2} - 36 a + 28\bigr] \)
25.2-a2 \( \bigl[a^{3} - a^{2} - 5 a\) , \( a^{3} - 2 a^{2} - 4 a + 2\) , \( -a^{3} + 2 a^{2} + 4 a\) , \( -214 a^{3} - 388 a^{2} - 41 a + 67\) , \( -7172 a^{3} - 13212 a^{2} - 1656 a + 2523\bigr] \)
25.2-a3 \( \bigl[a\) , \( -a^{3} + a^{2} + 5 a\) , \( -a^{3} + 2 a^{2} + 4 a - 1\) , \( -12 a^{3} + 8 a^{2} + 77 a - 17\) , \( 95 a^{3} - 189 a^{2} - 282 a + 147\bigr] \)
25.2-a4 \( \bigl[a\) , \( -a^{3} + a^{2} + 5 a\) , \( -a^{3} + 2 a^{2} + 4 a - 1\) , \( -2 a^{3} + 3 a^{2} + 7 a - 7\) , \( -a^{3} + a^{2} + 5 a - 1\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 10 & 5 \\ 2 & 1 & 5 & 10 \\ 10 & 5 & 1 & 2 \\ 5 & 10 & 2 & 1 \end{array}\right)\)

Isogeny graph