Properties

Base field 4.4.11661.1
Label 4.4.11661.1-27.10-b
Conductor 27.10
Rank \( 1 \)

Related objects

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Base field 4.4.11661.1

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

Elliptic curves in class 27.10-b over 4.4.11661.1

Isogeny class 27.10-b contains 2 curves linked by isogenies of degree 3.

Curve label Weierstrass Coefficients
27.10-b1 \( \bigl[a^{2} - 3\) , \( a^{3} - 2 a^{2} - 2 a + 3\) , \( a^{3} - 5 a - 1\) , \( 15 a^{3} - 51 a^{2} + 19 a + 33\) , \( -86 a^{3} + 317 a^{2} - 177 a - 159\bigr] \)
27.10-b2 \( \bigl[1\) , \( -a^{2} + 2 a + 2\) , \( a^{2} - a - 2\) , \( -4 a^{3} + 13 a^{2} - 5 a - 5\) , \( -13 a^{3} + 47 a^{2} - 25 a - 24\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph