Properties

Base field 5.5.24217.1
Label 5.5.24217.1-37.1-a
Conductor 37.1
Rank \( 0 \)

Related objects

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Base field 5.5.24217.1

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

Elliptic curves in class 37.1-a over 5.5.24217.1

Isogeny class 37.1-a contains only one elliptic curve.

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

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph