Properties

Base field 4.4.5725.1
Label 4.4.5725.1-9.1-a
Conductor 9.1
Rank \( 0 \)

Related objects

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Base field 4.4.5725.1

Generator \(a\), with minimal polynomial \( x^{4} - x^{3} - 8 x^{2} + 6 x + 11 \); class number \(1\).

Elliptic curves in class 9.1-a over 4.4.5725.1

Isogeny class 9.1-a contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
9.1-a1 \( \bigl[\frac{1}{3} a^{3} - \frac{5}{3} a + \frac{4}{3}\) , \( a^{2} - 3\) , \( \frac{1}{3} a^{3} - \frac{5}{3} a + \frac{4}{3}\) , \( \frac{5}{3} a^{3} + 3 a^{2} - \frac{31}{3} a - \frac{46}{3}\) , \( \frac{5}{3} a^{3} + 2 a^{2} - \frac{31}{3} a - \frac{34}{3}\bigr] \)
9.1-a2 \( \bigl[\frac{1}{3} a^{3} - \frac{5}{3} a + \frac{4}{3}\) , \( a^{2} - 3\) , \( \frac{1}{3} a^{3} - \frac{5}{3} a + \frac{4}{3}\) , \( -\frac{20}{3} a^{3} - 2 a^{2} + \frac{124}{3} a + \frac{49}{3}\) , \( \frac{25}{3} a^{3} + 2 a^{2} - \frac{170}{3} a - \frac{74}{3}\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph