Elliptic curve isogeny class 45.2-a over number field 4.4.4525.1

• Base field: 4.4.4525.1
• Label: 4.4.4525.1-45.2-a
• Conductor: 45.2
• 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 45.2-a over 4.4.4525.1

Isogeny class 45.2-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
45.2-a1	\( \bigl[\frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{4}{3} a - 3\) , \( \frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{10}{3} a - 4\) , \( a^{2} - a - 4\) , \( -\frac{140}{3} a^{3} - \frac{361}{3} a^{2} + \frac{368}{3} a + 218\) , \( \frac{1922}{3} a^{3} + \frac{3742}{3} a^{2} - \frac{4616}{3} a - 2355\bigr] \)
45.2-a2	\( \bigl[a^{2} - a - 3\) , \( -a^{2} + 3\) , \( a^{2} - a - 4\) , \( -\frac{11}{3} a^{3} + \frac{26}{3} a^{2} + \frac{53}{3} a - 35\) , \( -14 a^{3} + 31 a^{2} + 60 a - 112\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph