Properties

Base field 5.5.157457.1
Label 5.5.157457.1-15.1-b
Conductor 15.1
Rank \( 0 \)

Related objects

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Base field 5.5.157457.1

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

Elliptic curves in class 15.1-b over 5.5.157457.1

Isogeny class 15.1-b contains only one elliptic curve.

Curve label Weierstrass Coefficients
15.1-b1 \( \bigl[a^{3} - a^{2} - 3 a + 1\) , \( a^{4} - a^{3} - 4 a^{2} + a + 1\) , \( a^{3} - a^{2} - 2 a\) , \( a^{3} - a^{2} + 1\) , \( -20 a^{4} + 58 a^{3} + 33 a^{2} - 131 a + 23\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph