Properties

Base field 5.5.65657.1
Label 5.5.65657.1-27.1-c
Conductor 27.1
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 27.1-c over 5.5.65657.1

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

Curve label Weierstrass Coefficients
27.1-c1 \( \bigl[a^{2} - a - 1\) , \( 2 a^{4} - 2 a^{3} - 9 a^{2} + 4 a + 7\) , \( a + 1\) , \( 6 a^{4} - 15 a^{3} - 24 a^{2} + 36 a + 16\) , \( 18 a^{4} - 27 a^{3} - 60 a^{2} + 70 a + 21\bigr] \)
27.1-c2 \( \bigl[a^{2} - 2\) , \( -2 a^{4} + 2 a^{3} + 9 a^{2} - 5 a - 5\) , \( -a^{4} + a^{3} + 5 a^{2} - 3 a - 4\) , \( -3 a^{4} + 2 a^{3} + 13 a^{2} - a - 3\) , \( -18 a^{4} - 5 a^{3} + 80 a^{2} + 68 a + 10\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

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

Isogeny graph