Properties

Base field 4.4.4752.1
Label 4.4.4752.1-33.1-g
Conductor 33.1
Rank not recorded

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 33.1-g over 4.4.4752.1

Isogeny class 33.1-g contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
33.1-g1 \( \bigl[a^{3} - a^{2} - 3 a + 2\) , \( a^{2} - 2\) , \( 1\) , \( 6 a^{3} + 4 a^{2} - 10 a - 4\) , \( -123 a^{3} - 61 a^{2} + 217 a + 49\bigr] \)
33.1-g2 \( \bigl[a^{3} - a^{2} - 3 a + 2\) , \( a^{3} - 5 a - 2\) , \( 1\) , \( -5 a^{3} + 2 a^{2} + 14 a + 1\) , \( -8 a^{3} - 5 a^{2} + 11 a + 1\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

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

Isogeny graph