Properties

Base field 4.4.13888.1
Label 4.4.13888.1-28.1-a
Conductor 28.1
Rank \( 1 \)

Related objects

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Base field 4.4.13888.1

Generator \(a\), with minimal polynomial \( x^{4} - 2 x^{3} - 7 x^{2} + 6 x + 9 \); class number \(1\).

Elliptic curves in class 28.1-a over 4.4.13888.1

Isogeny class 28.1-a contains 2 curves linked by isogenies of degree 5.

Curve label Weierstrass Coefficients
28.1-a1 \( \bigl[a^{2} - 4\) , \( -\frac{1}{3} a^{3} - \frac{1}{3} a^{2} + \frac{7}{3} a + 4\) , \( \frac{1}{3} a^{3} - \frac{2}{3} a^{2} - \frac{1}{3} a + 2\) , \( -\frac{10}{3} a^{3} + \frac{26}{3} a^{2} + \frac{49}{3} a - 26\) , \( 4 a^{3} - 11 a^{2} - 16 a + 39\bigr] \)
28.1-a2 \( \bigl[a^{2} - 4\) , \( -\frac{1}{3} a^{3} - \frac{1}{3} a^{2} + \frac{7}{3} a + 4\) , \( \frac{1}{3} a^{3} - \frac{2}{3} a^{2} - \frac{1}{3} a + 2\) , \( \frac{65}{3} a^{3} - \frac{259}{3} a^{2} - \frac{311}{3} a + 269\) , \( -\frac{46}{3} a^{3} - \frac{166}{3} a^{2} - \frac{524}{3} a - 280\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph