Properties

Base field 3.3.316.1
Label 3.3.316.1-29.1-a
Conductor 29.1
Rank \( 0 \)

Related objects

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Base field 3.3.316.1

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

Elliptic curves in class 29.1-a over 3.3.316.1

Isogeny class 29.1-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
29.1-a1 \( \bigl[1\) , \( -a^{2} + 3\) , \( a^{2} + a - 3\) , \( 24658608 a^{2} - 13052210 a - 104777890\) , \( 97491816927 a^{2} - 51604035128 a - 414256431444\bigr] \)
29.1-a2 \( \bigl[1\) , \( -a^{2} + 3\) , \( a^{2} + a - 3\) , \( 1544963 a^{2} - 817775 a - 6564765\) , \( 1516590732 a^{2} - 802756621 a - 6444207162\bigr] \)
29.1-a3 \( \bigl[1\) , \( -a^{2} - a + 4\) , \( a\) , \( 26706469377 a^{2} - 14136177042 a - 113479541664\) , \( -1145144305880869 a^{2} + 606143867742873 a + 4865879092126621\bigr] \)
29.1-a4 \( \bigl[1\) , \( -a^{2} + a + 4\) , \( a\) , \( a^{2} - a - 4\) , \( 64 a^{2} - 34 a - 273\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph