Properties

Base field 4.4.4400.1
Label 4.4.4400.1-31.1-f
Conductor 31.1
Rank \( 1 \)

Related objects

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Base field 4.4.4400.1

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

Elliptic curves in class 31.1-f over 4.4.4400.1

Isogeny class 31.1-f contains only one elliptic curve.

Curve label Weierstrass Coefficients
31.1-f1 \( \bigl[a^{3} - 3 a\) , \( a^{3} - a^{2} - 3 a + 4\) , \( a^{3} - 3 a\) , \( -a^{3} + 4 a^{2} + 9 a - 20\) , \( -5 a^{3} + 12 a^{2} + 25 a - 49\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph