Properties

Base field 4.4.5125.1
Label 4.4.5125.1-41.1-a
Conductor 41.1
Rank \( 1 \)

Related objects

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Base field 4.4.5125.1

Generator \(a\), with minimal polynomial \( x^{4} - 2 x^{3} - 6 x^{2} + 7 x + 11 \); class number \(1\).

Elliptic curves in class 41.1-a over 4.4.5125.1

Isogeny class 41.1-a contains only one elliptic curve.

Curve label Weierstrass Coefficients
41.1-a1 \( \bigl[0\) , \( -a^{2} + 2 a + 3\) , \( a^{2} - 4\) , \( -6 a^{3} - 2 a^{2} + 25 a + 22\) , \( 8 a^{3} + 7 a^{2} - 30 a - 33\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph