Properties

Base field 4.4.5744.1
Label 4.4.5744.1-17.1-e
Conductor 17.1
Rank \( 1 \)

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-e over 4.4.5744.1

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

Curve label Weierstrass Coefficients
17.1-e1 \( \bigl[-a^{3} + a^{2} + 5 a - 1\) , \( -a^{2} + 3\) , \( a^{3} - 5 a\) , \( -23 a^{3} + 17 a^{2} + 100 a - 34\) , \( 58 a^{3} - 44 a^{2} - 257 a + 78\bigr] \)
17.1-e2 \( \bigl[-a^{3} + a^{2} + 5 a - 1\) , \( -a^{2} + 3\) , \( a^{3} - 5 a\) , \( 2 a^{3} - 3 a^{2} - 10 a + 6\) , \( -a^{3} + 4 a - 1\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph