Properties

Base field 4.4.2624.1
Label 4.4.2624.1-49.4-a
Conductor 49.4
Rank not recorded

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Base field 4.4.2624.1

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

Elliptic curves in class 49.4-a over 4.4.2624.1

Isogeny class 49.4-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label Weierstrass Coefficients
49.4-a1 \( \bigl[a^{3} - a^{2} - 3 a\) , \( a^{3} - a^{2} - 4 a + 1\) , \( a\) , \( 38 a^{3} - 41 a^{2} - 159 a - 66\) , \( -241 a^{3} + 276 a^{2} + 974 a + 319\bigr] \)
49.4-a2 \( \bigl[a^{3} - a^{2} - 3 a\) , \( a^{3} - a^{2} - 4 a + 1\) , \( a\) , \( 3 a^{3} - a^{2} - 9 a - 1\) , \( 3 a^{3} - 7 a - 2\bigr] \)
49.4-a3 \( \bigl[a^{3} - 2 a^{2} - 2 a + 1\) , \( -a^{3} + 2 a^{2} + 3 a - 2\) , \( a^{2} - 2 a\) , \( 4 a^{3} - 24 a^{2} - 22 a - 8\) , \( 4 a^{3} + 39 a^{2} + 126 a + 47\bigr] \)
49.4-a4 \( \bigl[a^{3} - 2 a^{2} - 2 a + 1\) , \( -a^{3} + 2 a^{2} + 3 a - 2\) , \( a^{2} - 2 a\) , \( -a^{3} + a^{2} + 3 a + 2\) , \( a^{3} - 2 a^{2} - 2 a - 1\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 2 & 6 \\ 3 & 1 & 6 & 2 \\ 2 & 6 & 1 & 3 \\ 6 & 2 & 3 & 1 \end{array}\right)\)

Isogeny graph