Properties

Base field 4.4.5744.1
Label 4.4.5744.1-4.1-b
Conductor 4.1
Rank \( 1 \)

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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 4.1-b over 4.4.5744.1

Isogeny class 4.1-b contains 2 curves linked by isogenies of degree 5.

Curve label Weierstrass Coefficients
4.1-b1 \( \bigl[a^{2} - 1\) , \( a^{2} - 2 a - 1\) , \( a^{3} - 5 a - 1\) , \( 2 a^{2} - a - 1\) , \( -a^{3} + 4 a^{2} - 4\bigr] \)
4.1-b2 \( \bigl[a + 1\) , \( -2 a^{3} + a^{2} + 9 a - 1\) , \( -a^{3} + a^{2} + 5 a\) , \( 62 a^{3} - 79 a^{2} - 175 a + 22\) , \( 511 a^{3} - 1071 a^{2} - 466 a + 283\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph