Properties

Base field 5.5.36497.1
Label 5.5.36497.1-49.1-a
Conductor 49.1
Rank not recorded

Related objects

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Base field 5.5.36497.1

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

Elliptic curves in class 49.1-a over 5.5.36497.1

Isogeny class 49.1-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
49.1-a1 \( \bigl[2 a^{4} - 3 a^{3} - 7 a^{2} + 7 a + 4\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 6 a + 2\) , \( a^{2} - 2\) , \( -127 a^{4} + 191 a^{3} + 470 a^{2} - 400 a - 351\) , \( -1617 a^{4} + 2597 a^{3} + 5876 a^{2} - 5786 a - 3783\bigr] \)
49.1-a2 \( \bigl[a^{4} - 2 a^{3} - 3 a^{2} + 6 a + 2\) , \( 2 a^{4} - 3 a^{3} - 8 a^{2} + 9 a + 5\) , \( 2 a^{4} - 3 a^{3} - 6 a^{2} + 7 a + 2\) , \( 10 a^{4} - 17 a^{3} - 35 a^{2} + 39 a + 24\) , \( 16 a^{4} - 27 a^{3} - 54 a^{2} + 56 a + 36\bigr] \)
49.1-a3 \( \bigl[2 a^{4} - 3 a^{3} - 7 a^{2} + 7 a + 4\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 6 a + 2\) , \( a^{2} - 2\) , \( -32 a^{4} + 46 a^{3} + 115 a^{2} - 100 a - 76\) , \( 40 a^{4} - 60 a^{3} - 144 a^{2} + 132 a + 97\bigr] \)
49.1-a4 \( \bigl[a + 1\) , \( a^{4} - a^{3} - 3 a^{2} + 1\) , \( 2 a^{4} - 3 a^{3} - 7 a^{2} + 7 a + 3\) , \( 9 a^{4} + 37 a^{3} - 134 a^{2} - 23 a + 26\) , \( -112 a^{4} - 62 a^{3} + 868 a^{2} - 258 a - 38\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

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

Isogeny graph