Properties

Base field 5.5.65657.1
Label 5.5.65657.1-25.1-a
Conductor 25.1
Rank not recorded

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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 25.1-a over 5.5.65657.1

Isogeny class 25.1-a contains only one elliptic curve.

Curve label Weierstrass Coefficients
25.1-a1 \( \bigl[-2 a^{4} + 3 a^{3} + 9 a^{2} - 9 a - 6\) , \( -a^{2} + 3\) , \( a^{3} - 3 a - 1\) , \( a^{4} + 3 a^{3} - 8 a^{2} - 15 a + 8\) , \( -2 a^{4} + 3 a^{3} + 6 a^{2} - 5 a + 6\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

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

Isogeny graph