Properties

Base field 4.4.5125.1
Label 4.4.5125.1-19.1-b
Conductor 19.1
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 19.1-b over 4.4.5125.1

Isogeny class 19.1-b contains only one elliptic curve.

Curve label Weierstrass Coefficients
19.1-b1 \( \bigl[0\) , \( -a^{3} + 6 a + 4\) , \( a^{2} - 3\) , \( -7 a^{3} - 4 a^{2} + 32 a + 32\) , \( 11 a^{3} + 9 a^{2} - 43 a - 45\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph