Properties

Base field 5.5.36497.1
Label 5.5.36497.1-27.1-a
Conductor 27.1
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 27.1-a over 5.5.36497.1

Isogeny class 27.1-a contains 2 curves linked by isogenies of degree 3.

Curve label Weierstrass Coefficients
27.1-a1 \( \bigl[a^{2} - 2\) , \( -a^{4} + 2 a^{3} + 3 a^{2} - 6 a - 1\) , \( a^{4} - a^{3} - 4 a^{2} + 2 a + 2\) , \( -a^{2} + 3\) , \( -1\bigr] \)
27.1-a2 \( \bigl[a^{4} - a^{3} - 3 a^{2} + 2 a\) , \( a^{2} - a - 2\) , \( 2 a^{4} - 3 a^{3} - 6 a^{2} + 7 a + 1\) , \( 374 a^{4} - 252 a^{3} - 1451 a^{2} - 59 a + 277\) , \( 5982 a^{4} - 3984 a^{3} - 23258 a^{2} - 1118 a + 4479\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph