Properties

Base field 4.4.19525.1
Label 4.4.19525.1-19.2-a
Conductor 19.2
Rank \( 1 \)

Related objects

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Base field 4.4.19525.1

Generator \(a\), with minimal polynomial \( x^{4} - 2 x^{3} - 14 x^{2} + 15 x + 45 \); class number \(1\).

Elliptic curves in class 19.2-a over 4.4.19525.1

Isogeny class 19.2-a contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
19.2-a1 \( \bigl[\frac{1}{3} a^{3} - \frac{10}{3} a - 3\) , \( -\frac{1}{3} a^{3} + \frac{7}{3} a + 3\) , \( \frac{1}{3} a^{2} + \frac{2}{3} a - 2\) , \( -2 a^{3} - a^{2} + 24 a + 34\) , \( -4 a^{3} - \frac{8}{3} a^{2} + \frac{146}{3} a + 67\bigr] \)
19.2-a2 \( \bigl[a + 1\) , \( \frac{1}{3} a^{3} - \frac{2}{3} a^{2} - \frac{8}{3} a + 2\) , \( a + 1\) , \( \frac{2}{3} a^{3} - \frac{32}{3} a - 11\) , \( -a^{3} - \frac{32}{3} a^{2} + \frac{71}{3} a + 62\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph