Properties

Base field 4.4.13888.1
Label 4.4.13888.1-28.1-c
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-c over 4.4.13888.1

Isogeny class 28.1-c contains 2 curves linked by isogenies of degree 3.

Curve label Weierstrass Coefficients
28.1-c1 \( \bigl[\frac{1}{3} a^{3} + \frac{1}{3} a^{2} - \frac{7}{3} a - 3\) , \( 1\) , \( a^{2} - 4\) , \( -\frac{8}{3} a^{3} + \frac{19}{3} a^{2} + \frac{41}{3} a - 17\) , \( -\frac{40}{3} a^{3} + \frac{113}{3} a^{2} + \frac{181}{3} a - 125\bigr] \)
28.1-c2 \( \bigl[\frac{1}{3} a^{3} - \frac{2}{3} a^{2} - \frac{1}{3} a + 1\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - \frac{10}{3} a - 2\) , \( 1\) , \( -\frac{2}{3} a^{3} + \frac{10}{3} a^{2} + \frac{5}{3} a\) , \( \frac{1}{3} a^{3} + \frac{4}{3} a^{2} - \frac{13}{3} a - 2\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph