Properties

Base field 5.5.70601.1
Label 5.5.70601.1-32.1-b
Conductor 32.1
Rank \( 1 \)

Related objects

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Base field 5.5.70601.1

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

Elliptic curves in class 32.1-b over 5.5.70601.1

Isogeny class 32.1-b contains only one elliptic curve.

Curve label Weierstrass Coefficients
32.1-b1 \( \bigl[2 a^{4} - a^{3} - 11 a^{2} + a + 5\) , \( -a^{4} + a^{3} + 5 a^{2} - 3 a - 3\) , \( 3 a^{4} - 2 a^{3} - 15 a^{2} + a + 5\) , \( 9 a^{4} - 4 a^{3} - 39 a^{2} - 20 a + 3\) , \( -31 a^{4} + a^{3} + 170 a^{2} + 75 a - 45\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{r} 1 \end{array}\right)\)

Isogeny graph