Properties

Base field 4.4.15125.1
Label 4.4.15125.1-19.3-a
Conductor 19.3
Rank \( 1 \)

Related objects

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Base field 4.4.15125.1

Generator \(a\), with minimal polynomial \( x^{4} - x^{3} - 14 x^{2} + 14 x + 31 \); class number \(1\).

Elliptic curves in class 19.3-a over 4.4.15125.1

Isogeny class 19.3-a contains only one elliptic curve.

Curve label Weierstrass Coefficients
19.3-a1 \( \bigl[a^{3} + 2 a^{2} - 8 a - 13\) , \( 4 a^{3} + 7 a^{2} - 37 a - 43\) , \( -2 a^{3} - 3 a^{2} + 18 a + 17\) , \( -6 a^{3} + a^{2} + 39 a + 27\) , \( -a^{3} + 41 a^{2} - 62 a - 132\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph