Properties

Base field 4.4.4525.1
Label 4.4.4525.1-25.3-a
Conductor 25.3
Rank \( 0 \)

Related objects

Learn more about

Base field 4.4.4525.1

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

Elliptic curves in class 25.3-a over 4.4.4525.1

Isogeny class 25.3-a contains 2 curves linked by isogenies of degree 3.

Curve label Weierstrass Coefficients
25.3-a1 \( \bigl[\frac{1}{3} a^{3} - \frac{1}{3} a^{2} - \frac{4}{3} a\) , \( a^{2} - 5\) , \( \frac{1}{3} a^{3} - \frac{1}{3} a^{2} - \frac{1}{3} a\) , \( -\frac{7}{3} a^{3} + \frac{19}{3} a^{2} + \frac{13}{3} a - 11\) , \( -\frac{1}{3} a^{3} + \frac{1}{3} a^{2} + \frac{4}{3} a - 2\bigr] \)
25.3-a2 \( \bigl[\frac{1}{3} a^{3} - \frac{1}{3} a^{2} - \frac{1}{3} a\) , \( -\frac{1}{3} a^{3} - \frac{2}{3} a^{2} + \frac{10}{3} a + 3\) , \( \frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{4}{3} a - 3\) , \( 2 a^{3} + 3 a^{2} - a - 2\) , \( \frac{17}{3} a^{3} + \frac{28}{3} a^{2} - \frac{35}{3} a - 17\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph