Properties

Base field 4.4.4752.1
Label 4.4.4752.1-23.1-b
Conductor 23.1
Rank \( 1 \)

Related objects

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Base field 4.4.4752.1

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

Elliptic curves in class 23.1-b over 4.4.4752.1

Isogeny class 23.1-b contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
23.1-b1 \( \bigl[a^{3} - 4 a - 1\) , \( -a^{3} + a^{2} + 2 a\) , \( a^{2} - a - 2\) , \( -3 a^{3} + 2 a^{2} + 9 a + 1\) , \( -2 a^{3} + a^{2} + 7 a + 2\bigr] \)
23.1-b2 \( \bigl[a^{2} - a - 1\) , \( -a^{3} + 2 a^{2} + 2 a - 4\) , \( a^{3} - 4 a\) , \( 6 a^{3} - 21 a^{2} + 8 a + 9\) , \( -28 a^{3} + 96 a^{2} - 60 a - 21\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph