Properties

Base field 4.4.725.1
Label 4.4.725.1-79.2-a
Conductor 79.2
Rank not recorded

Related objects

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Base field 4.4.725.1

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

Elliptic curves in class 79.2-a over 4.4.725.1

Isogeny class 79.2-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
79.2-a1 \( \bigl[a^{3} - 3 a\) , \( a^{3} - 2 a^{2} - a + 3\) , \( a^{3} - 3 a + 1\) , \( -195 a^{3} + 234 a^{2} + 421 a - 359\) , \( -1610 a^{3} + 2626 a^{2} + 3852 a - 3624\bigr] \)
79.2-a2 \( \bigl[a^{3} - 3 a\) , \( a^{3} - 2 a^{2} - a + 3\) , \( a^{3} - 3 a + 1\) , \( -10 a^{3} + 9 a^{2} + 26 a - 19\) , \( -34 a^{3} + 49 a^{2} + 83 a - 74\bigr] \)
79.2-a3 \( \bigl[a^{3} - 3 a\) , \( a^{3} - 2 a^{2} - a + 3\) , \( a^{3} - 3 a + 1\) , \( -a^{2} + a + 1\) , \( -a^{3} + a^{2} + 3 a - 2\bigr] \)
79.2-a4 \( \bigl[a^{3} - 3 a\) , \( a^{3} - 2 a^{2} - a + 3\) , \( a^{3} - 3 a + 1\) , \( 15 a^{3} - 56 a^{2} + 31 a + 1\) , \( 90 a^{3} - 276 a^{2} + 114 a + 28\bigr] \)

Rank

Rank not yet determined.

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