Elliptic curve isogeny class 44.3-d over number field 4.4.8000.1

• Base field: 4.4.8000.1
• Label: 4.4.8000.1-44.3-d
• Conductor: 44.3
• Rank: \( 1 \)

Base field 4.4.8000.1

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

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph

Elliptic curves in class 44.3-d over 4.4.8000.1

Isogeny class 44.3-d contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
44.3-d1	\( \bigl[\frac{1}{2} a^{2} - 3\) , \( \frac{1}{2} a^{2} + a - 2\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 2 a - 2\) , \( -\frac{319}{2} a^{3} - \frac{447}{2} a^{2} + 1339 a + 2112\) , \( -2071 a^{3} - \frac{11387}{2} a^{2} + 5194 a + 14855\bigr] \)
44.3-d2	\( \bigl[\frac{1}{2} a^{2} - 3\) , \( -\frac{1}{2} a^{3} + 4 a - 1\) , \( \frac{1}{2} a^{3} - 3 a\) , \( 2 a^{3} - \frac{9}{2} a^{2} - 13 a + 28\) , \( -\frac{3}{2} a^{3} + \frac{3}{2} a^{2} + 14 a - 20\bigr] \)