Properties

Base field 4.4.8069.1
Label 4.4.8069.1-5.1-b
Conductor 5.1
Rank \( 1 \)

Related objects

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Base field 4.4.8069.1

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

Elliptic curves in class 5.1-b over 4.4.8069.1

Isogeny class 5.1-b contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
5.1-b1 \( \bigl[a^{3} + a^{2} - 4 a - 1\) , \( -1\) , \( a + 1\) , \( 69 a^{3} + 16 a^{2} - 324 a - 58\) , \( -456 a^{3} - 106 a^{2} + 2148 a + 372\bigr] \)
5.1-b2 \( \bigl[a^{3} + a^{2} - 4 a - 1\) , \( -1\) , \( a + 1\) , \( 4 a^{3} + a^{2} - 19 a - 3\) , \( -5 a^{3} - a^{2} + 24 a + 4\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph