Properties

Base field 5.5.65657.1
Label 5.5.65657.1-5.1-a
Conductor 5.1
Rank not recorded

Related objects

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Base field 5.5.65657.1

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

Elliptic curves in class 5.1-a over 5.5.65657.1

Isogeny class 5.1-a contains only one elliptic curve.

Curve label Weierstrass Coefficients
5.1-a1 \( \bigl[-a^{4} + 2 a^{3} + 4 a^{2} - 5 a - 3\) , \( -a^{4} + a^{3} + 4 a^{2} - 3 a - 1\) , \( a^{4} - a^{3} - 4 a^{2} + 3 a + 2\) , \( -3 a^{4} + 2 a^{3} + 10 a^{2} - 7 a - 3\) , \( a^{4} + 3 a^{3} - 6 a - 3\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

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

Isogeny graph