Properties

Base field 4.4.8112.1
Label 4.4.8112.1-17.2-b
Conductor 17.2
Rank \( 1 \)

Related objects

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Base field 4.4.8112.1

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

Elliptic curves in class 17.2-b over 4.4.8112.1

Isogeny class 17.2-b contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
17.2-b1 \( \bigl[a^{2} - 2\) , \( -a^{3} + 4 a\) , \( a^{2} - 2\) , \( -6 a^{3} + 4 a^{2} + 24 a - 23\) , \( 21 a^{3} - 15 a^{2} - 89 a + 66\bigr] \)
17.2-b2 \( \bigl[a^{2} - 2\) , \( -a^{3} + 4 a\) , \( a^{2} - 2\) , \( -a^{3} - a^{2} + 4 a + 2\) , \( -a^{2} + 3\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph