Properties

Base field 4.4.5744.1
Label 4.4.5744.1-28.1-c
Conductor 28.1
Rank \( 0 \)

Related objects

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Base field 4.4.5744.1

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

Elliptic curves in class 28.1-c over 4.4.5744.1

Isogeny class 28.1-c contains 2 curves linked by isogenies of degree 5.

Curve label Weierstrass Coefficients
28.1-c1 \( \bigl[a + 1\) , \( a^{3} - 6 a - 1\) , \( 1\) , \( 71 a^{3} - 54 a^{2} - 85 a - 45\) , \( 333 a^{3} - 918 a^{2} + 158 a - 164\bigr] \)
28.1-c2 \( \bigl[a + 1\) , \( a^{3} - 6 a - 1\) , \( 1\) , \( -4 a^{3} - 4 a^{2} + 5 a\) , \( 7 a^{3} + 14 a^{2} - 2\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph