Properties

Base field 4.4.9792.1
Label 4.4.9792.1-23.2-a
Conductor 23.2
Rank \( 1 \)

Related objects

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Base field 4.4.9792.1

Generator \(a\), with minimal polynomial \( x^{4} - 2 x^{3} - 7 x^{2} + 2 x + 7 \); class number \(1\).

Elliptic curves in class 23.2-a over 4.4.9792.1

Isogeny class 23.2-a contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
23.2-a1 \( \bigl[a^{2} - a - 3\) , \( a^{2} - 2 a - 3\) , \( a^{2} - 2 a - 3\) , \( a^{3} + a^{2} - 4 a - 4\) , \( a^{3} - 3 a - 2\bigr] \)
23.2-a2 \( \bigl[a^{3} - 3 a^{2} - 3 a + 4\) , \( a - 1\) , \( a^{3} - 3 a^{2} - 2 a + 5\) , \( 0\) , \( -a^{2} + 1\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph