Properties

Base field 5.5.36497.1
Label 5.5.36497.1-49.1-b
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-b over 5.5.36497.1

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

Curve label Weierstrass Coefficients
49.1-b1 \( \bigl[2 a^{4} - 3 a^{3} - 6 a^{2} + 6 a + 1\) , \( a^{4} - a^{3} - 4 a^{2} + 3 a + 2\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 6 a + 1\) , \( 2 a^{4} - 3 a^{3} + 5 a^{2} + a - 44\) , \( 20 a^{4} - 15 a^{3} - 37 a^{2} - 26 a - 133\bigr] \)
49.1-b2 \( \bigl[2 a^{4} - 3 a^{3} - 6 a^{2} + 6 a + 1\) , \( a^{4} - a^{3} - 4 a^{2} + 3 a + 2\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 6 a + 1\) , \( 2 a^{4} - 3 a^{3} - 5 a^{2} + 6 a + 1\) , \( 2 a^{4} - 2 a^{3} - 7 a^{2} + 4 a + 2\bigr] \)
49.1-b3 \( \bigl[2 a^{4} - 3 a^{3} - 6 a^{2} + 6 a + 1\) , \( a^{4} - a^{3} - 4 a^{2} + 3 a + 2\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 6 a + 1\) , \( 7 a^{4} - 3 a^{3} - 25 a^{2} - 9 a - 4\) , \( 32 a^{4} - 23 a^{3} - 123 a^{2} + 22\bigr] \)
49.1-b4 \( \bigl[a^{4} - a^{3} - 4 a^{2} + 3 a + 3\) , \( -2 a^{4} + 3 a^{3} + 7 a^{2} - 8 a - 2\) , \( 0\) , \( -15 a^{4} + 15 a^{3} + 36 a^{2} - 32 a - 19\) , \( -15 a^{4} - 48 a^{3} - 18 a^{2} + 125 a + 13\bigr] \)

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