Elliptic curve isogeny class 45.4-a over number field 4.4.4525.1

• Base field: 4.4.4525.1
• Label: 4.4.4525.1-45.4-a
• Conductor: 45.4
• Rank: \( 1 \)

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 45.4-a over 4.4.4525.1

Isogeny class 45.4-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
45.4-a1	\( \bigl[\frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{4}{3} a - 4\) , \( \frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{4}{3} a - 4\) , \( a + 1\) , \( 7 a^{3} + a^{2} - 53 a - 53\) , \( 68 a^{3} + 20 a^{2} - 466 a - 448\bigr] \)
45.4-a2	\( \bigl[1\) , \( \frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{4}{3} a - 4\) , \( 1\) , \( -\frac{65}{3} a^{3} + \frac{155}{3} a^{2} + \frac{296}{3} a - 209\) , \( -156 a^{3} + 334 a^{2} + 727 a - 1306\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph