Properties

Base field 3.3.49.1
Label 3.3.49.1-27.1-a
Conductor 27.1
Rank not recorded

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Base field 3.3.49.1

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

Elliptic curves in class 27.1-a over 3.3.49.1

Isogeny class 27.1-a contains 2 curves linked by isogenies of degree 13.

Curve label Weierstrass Coefficients
27.1-a1 \( \bigl[0\) , \( -a\) , \( a\) , \( 652 a^{2} - 391 a - 1564\) , \( 10528 a^{2} - 5979 a - 24046\bigr] \)
27.1-a2 \( \bigl[0\) , \( -a\) , \( a\) , \( 2 a^{2} - a - 4\) , \( -2 a^{2} + a + 4\bigr] \)

Rank

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Isogeny matrix

\(\left(\begin{array}{rr} 1 & 13 \\ 13 & 1 \end{array}\right)\)

Isogeny graph