Properties

Base field 4.4.5744.1
Label 4.4.5744.1-17.1-b
Conductor 17.1
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 17.1-b over 4.4.5744.1

Isogeny class 17.1-b contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
17.1-b1 \( \bigl[a^{2} - 1\) , \( 2 a^{3} - a^{2} - 9 a + 1\) , \( -a^{3} + a^{2} + 4 a - 1\) , \( 14 a^{3} - 2 a^{2} - 62 a - 27\) , \( 21 a^{3} + 5 a^{2} - 106 a - 67\bigr] \)
17.1-b2 \( \bigl[a + 1\) , \( a^{2} - a - 1\) , \( a^{3} - 5 a - 1\) , \( -3 a^{3} + 4 a^{2} + 12 a - 3\) , \( a^{3} + a^{2} - 6 a\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph