Properties

Base field 4.4.4525.1
Label 4.4.4525.1-25.1-b
Conductor 25.1
Rank \( 1 \)

Related objects

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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 25.1-b over 4.4.4525.1

Isogeny class 25.1-b contains 2 curves linked by isogenies of degree 3.

Curve label Weierstrass Coefficients
25.1-b1 \( \bigl[a^{2} - 3\) , \( \frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{7}{3} a - 5\) , \( a\) , \( a^{3} - 6 a^{2} + 5 a + 14\) , \( -\frac{10}{3} a^{3} + \frac{40}{3} a^{2} - \frac{5}{3} a - 23\bigr] \)
25.1-b2 \( \bigl[\frac{1}{3} a^{3} - \frac{1}{3} a^{2} - \frac{4}{3} a + 1\) , \( \frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{10}{3} a - 5\) , \( \frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{4}{3} a - 3\) , \( -a^{3} - 3 a^{2} + 10 a + 12\) , \( \frac{8}{3} a^{3} - \frac{14}{3} a^{2} - \frac{26}{3} a - 2\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph