Properties

Base field 4.4.15188.1
Label 4.4.15188.1-16.4-b
Conductor 16.4
Rank \( 1 \)

Related objects

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Base field 4.4.15188.1

Generator \(a\), with minimal polynomial \( x^{4} - x^{3} - 7 x^{2} + x + 2 \); class number \(1\).

Elliptic curves in class 16.4-b over 4.4.15188.1

Isogeny class 16.4-b contains only one elliptic curve.

Curve label Weierstrass Coefficients
16.4-b1 \( \bigl[a^{3} - a^{2} - 5 a\) , \( a^{3} - a^{2} - 6 a\) , \( \frac{1}{2} a^{3} - \frac{7}{2} a - 1\) , \( a^{3} - 8 a\) , \( \frac{1}{2} a^{3} - \frac{7}{2} a\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph