Properties

Base field 4.4.11661.1
Label 4.4.11661.1-27.1-e
Conductor 27.1
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 27.1-e over 4.4.11661.1

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

Curve label Weierstrass Coefficients
27.1-e1 \( \bigl[a^{2} - a - 2\) , \( a^{3} - a^{2} - 5 a\) , \( a^{2} - 3\) , \( -22 a^{3} + 46 a^{2} + 68 a - 105\) , \( -106 a^{3} - 64 a^{2} + 626 a + 732\bigr] \)
27.1-e2 \( \bigl[a^{3} - a^{2} - 4 a + 2\) , \( a^{3} - 6 a - 3\) , \( a^{2} - a - 2\) , \( -9 a^{3} + 18 a^{2} + 30 a - 42\) , \( 19 a^{3} - 44 a^{2} - 57 a + 107\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph