Elliptic curve isogeny class 44.1-d over number field 4.4.8000.1

• Base field: 4.4.8000.1
• Label: 4.4.8000.1-44.1-d
• Conductor: 44.1
• Rank: \( 1 \)

Base field 4.4.8000.1

Generator \(a\), with minimal polynomial \( x^{4} - 10 x^{2} + 20 \); class number \(1\).

Elliptic curves in class 44.1-d over 4.4.8000.1

Isogeny class 44.1-d contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
44.1-d1	\( \bigl[\frac{1}{2} a^{2} - 2\) , \( \frac{1}{2} a^{3} - 2 a - 1\) , \( a\) , \( -\frac{1}{2} a^{3} + \frac{9}{2} a^{2} - a - 17\) , \( \frac{5}{2} a^{3} - \frac{3}{2} a^{2} - 12 a - 5\bigr] \)
44.1-d2	\( \bigl[\frac{1}{2} a^{2} - 2\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 3 a + 3\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 2 a - 3\) , \( 191 a^{3} + \frac{447}{2} a^{2} - 828 a - 123\) , \( -\frac{7231}{2} a^{3} + \frac{11383}{2} a^{2} + 25834 a - 42070\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph