Elliptic curve isogeny class 9.2-a over number field 4.4.5725.1

• Base field: 4.4.5725.1
• Label: 4.4.5725.1-9.2-a
• Conductor: 9.2
• Rank: \( 0 \)

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 9.2-a over 4.4.5725.1

Isogeny class 9.2-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
9.2-a1	\( \bigl[\frac{1}{3} a^{3} - \frac{5}{3} a + \frac{1}{3}\) , \( -a^{2} + a + 5\) , \( \frac{1}{3} a^{3} - \frac{5}{3} a + \frac{1}{3}\) , \( -\frac{28}{3} a^{3} + 30 a^{2} - \frac{10}{3} a - \frac{103}{3}\) , \( 51 a^{3} - 178 a^{2} + 33 a + 227\bigr] \)
9.2-a2	\( \bigl[\frac{1}{3} a^{3} - \frac{5}{3} a + \frac{4}{3}\) , \( -\frac{1}{3} a^{3} - a^{2} + \frac{5}{3} a + \frac{8}{3}\) , \( 0\) , \( \frac{2}{3} a^{3} - a^{2} - \frac{4}{3} a + \frac{5}{3}\) , \( 0\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph