Elliptic curve isogeny class 45.4-b over number field 4.4.4525.1

• Base field: 4.4.4525.1
• Label: 4.4.4525.1-45.4-b
• 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-b over 4.4.4525.1

Isogeny class 45.4-b contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
45.4-b1	\( \bigl[a^{2} - a - 4\) , \( -a^{2} + a + 5\) , \( \frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{4}{3} a - 3\) , \( -\frac{44}{3} a^{3} + \frac{86}{3} a^{2} + \frac{209}{3} a - 108\) , \( 56 a^{3} - 120 a^{2} - 262 a + 467\bigr] \)
45.4-b2	\( \bigl[1\) , \( a^{2} - a - 4\) , \( \frac{1}{3} a^{3} - \frac{1}{3} a^{2} - \frac{4}{3} a + 1\) , \( -a^{3} + 5 a + 4\) , \( \frac{20}{3} a^{3} + \frac{10}{3} a^{2} - \frac{128}{3} a - 43\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph