Properties

Base field 6.6.1683101.1
Label 6.6.1683101.1-41.2-a
Conductor 41.2
Rank \( 2 \)

Related objects

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Base field 6.6.1683101.1

Generator \(a\), with minimal polynomial \( x^{6} - 3 x^{5} - 4 x^{4} + 13 x^{3} + 7 x^{2} - 14 x - 7 \); class number \(1\).

Elliptic curves in class 41.2-a over 6.6.1683101.1

Isogeny class 41.2-a contains only one elliptic curve.

Curve label Weierstrass Coefficients
41.2-a1 \( \bigl[a^{3} - a^{2} - 2 a\) , \( a^{5} - 3 a^{4} - 2 a^{3} + 9 a^{2} - 4\) , \( a^{4} - a^{3} - 4 a^{2} + 2 a + 3\) , \( 0\) , \( 0\bigr] \)

Rank

Rank: \( 2 \)

Isogeny matrix

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

Isogeny graph