Properties

Base field 4.4.7168.1
Label 4.4.7168.1-34.1-a
Conductor 34.1
Rank \( 1 \)

Related objects

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Base field 4.4.7168.1

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

Elliptic curves in class 34.1-a over 4.4.7168.1

Isogeny class 34.1-a contains only one elliptic curve.

Curve label Weierstrass Coefficients
34.1-a1 \( \bigl[a^{2} + a - 3\) , \( a^{3} + a^{2} - 5 a - 3\) , \( a^{3} + a^{2} - 4 a - 2\) , \( -a^{3} - 2 a^{2} + 4 a + 11\) , \( 3 a^{3} + 5 a^{2} - 9 a - 13\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph