Properties

Base field 5.5.36497.1
Label 5.5.36497.1-13.1-b
Conductor 13.1
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 13.1-b over 5.5.36497.1

Isogeny class 13.1-b contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
13.1-b1 \( \bigl[1\) , \( 2 a^{4} - 3 a^{3} - 7 a^{2} + 6 a + 2\) , \( 0\) , \( 8 a^{4} - 12 a^{3} - 28 a^{2} + 24 a + 12\) , \( 10 a^{4} - 19 a^{3} - 39 a^{2} + 50 a + 43\bigr] \)
13.1-b2 \( \bigl[1\) , \( 2 a^{4} - 3 a^{3} - 7 a^{2} + 6 a + 2\) , \( 0\) , \( -2 a^{4} + 3 a^{3} + 7 a^{2} - 6 a - 3\) , \( 0\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

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

Isogeny graph