Properties

Base field 4.4.14272.1
Label 4.4.14272.1-23.1-b
Conductor 23.1
Rank \( 1 \)

Related objects

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Base field 4.4.14272.1

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

Elliptic curves in class 23.1-b over 4.4.14272.1

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

Curve label Weierstrass Coefficients
23.1-b1 \( \bigl[a^{3} - 3 a^{2} - a + 4\) , \( a^{3} - 3 a^{2} - 2 a + 2\) , \( a^{3} - 2 a^{2} - 4 a + 2\) , \( -a^{2} + 2 a + 1\) , \( -a^{3} + 4 a^{2} - 4\bigr] \)
23.1-b2 \( \bigl[2 a^{3} - 5 a^{2} - 5 a + 5\) , \( -a^{3} + 3 a^{2} + 3 a - 4\) , \( 2 a^{3} - 5 a^{2} - 5 a + 4\) , \( -a^{3} + 4 a^{2} + 3 a - 9\) , \( a^{2} - 4\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph