Elliptic curve isogeny class 9.1-a over number field 4.4.4525.1

• Base field: 4.4.4525.1
• Label: 4.4.4525.1-9.1-a
• Conductor: 9.1
• Rank: \( 0 \)

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 9.1-a over 4.4.4525.1

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

Curve label	Weierstrass Coefficients
9.1-a1	\( \bigl[\frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{7}{3} a - 3\) , \( -a^{2} + 4\) , \( a^{2} - 3\) , \( -\frac{61}{3} a^{3} + \frac{124}{3} a^{2} + \frac{286}{3} a - 160\) , \( \frac{257}{3} a^{3} - \frac{542}{3} a^{2} - \frac{1205}{3} a + 700\bigr] \)
9.1-a2	\( \bigl[\frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{7}{3} a - 3\) , \( -a^{2} + 4\) , \( a^{2} - 3\) , \( -\frac{11}{3} a^{3} + \frac{14}{3} a^{2} + \frac{56}{3} a - 15\) , \( -\frac{22}{3} a^{3} + \frac{37}{3} a^{2} + \frac{106}{3} a - 45\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph