Properties

Base field 4.4.725.1
Label 4.4.725.1-41.2-a
Conductor 41.2
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 41.2-a over 4.4.725.1

Isogeny class 41.2-a contains 4 curves linked by isogenies of degrees dividing 14.

Curve label Weierstrass Coefficients
41.2-a1 \( \bigl[a^{3} - a^{2} - a + 2\) , \( a^{3} - 4 a\) , \( 1\) , \( -135 a^{3} + 127 a^{2} + 515 a - 400\) , \( -1476 a^{3} + 1408 a^{2} + 5442 a - 4190\bigr] \)
41.2-a2 \( \bigl[a^{3} - a^{2} - a + 2\) , \( a^{3} - 4 a\) , \( 1\) , \( -5 a^{3} - 3 a^{2} + 20 a - 10\) , \( 2 a^{3} + 7 a^{2} - 18 a + 8\bigr] \)
41.2-a3 \( \bigl[a^{3} - a^{2} - a + 2\) , \( a^{3} - 4 a\) , \( 1\) , \( 2 a^{2}\) , \( 2 a^{2} - a - 1\bigr] \)
41.2-a4 \( \bigl[a^{3} - a^{2} - a + 2\) , \( a^{3} - 4 a\) , \( 1\) , \( 1080 a^{3} - 2888 a^{2} + 790 a + 550\) , \( 46346 a^{3} - 112940 a^{2} + 15137 a + 31683\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 14 & 7 & 2 \\ 14 & 1 & 2 & 7 \\ 7 & 2 & 1 & 14 \\ 2 & 7 & 14 & 1 \end{array}\right)\)

Isogeny graph