Properties

Base field 4.4.4205.1
Label 4.4.4205.1-49.2-a
Conductor 49.2
Rank not recorded

Related objects

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Base field 4.4.4205.1

Generator \(a\), with minimal polynomial \( x^{4} - x^{3} - 5 x^{2} - x + 1 \); class number \(1\).

Elliptic curves in class 49.2-a over 4.4.4205.1

Isogeny class 49.2-a contains 4 curves linked by isogenies of degrees dividing 10.

Curve label Weierstrass Coefficients
49.2-a1 \( \bigl[a^{3} - a^{2} - 4 a - 1\) , \( 0\) , \( 0\) , \( -4 a^{3} + 4 a^{2} + 24 a - 8\) , \( -a^{3} + a^{2} + 6 a - 1\bigr] \)
49.2-a2 \( \bigl[a^{3} - a^{2} - 4 a - 1\) , \( 0\) , \( 0\) , \( a^{3} - a^{2} - 6 a + 2\) , \( 0\bigr] \)
49.2-a3 \( \bigl[1\) , \( a^{3} - a^{2} - 6 a - 2\) , \( 0\) , \( -27\) , \( 15 a^{3} - 15 a^{2} - 90 a - 5\bigr] \)
49.2-a4 \( \bigl[1\) , \( a^{3} - a^{2} - 6 a - 2\) , \( 0\) , \( 5 a^{3} - 5 a^{2} - 30 a - 17\) , \( 6 a^{3} - 6 a^{2} - 36 a - 19\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)\)

Isogeny graph