Elliptic curve isogeny class 44.1-a over number field 4.4.8000.1

• Base field: 4.4.8000.1
• Label: 4.4.8000.1-44.1-a
• Conductor: 44.1
• Rank: \( 0 \)

Base field 4.4.8000.1

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

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph

Elliptic curves in class 44.1-a over 4.4.8000.1

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

Curve label	Weierstrass Coefficients
44.1-a1	\( \bigl[a + 1\) , \( -\frac{1}{2} a^{2} - a + 3\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 2 a - 2\) , \( 9 a^{3} + 7 a^{2} - 47 a - 44\) , \( -10 a^{3} - 16 a^{2} + 61 a + 151\bigr] \)
44.1-a2	\( \bigl[a + 1\) , \( -\frac{1}{2} a^{2} - a + 3\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 2 a - 2\) , \( -a^{3} - 3 a^{2} + 3 a + 11\) , \( -a^{3} - \frac{5}{2} a^{2} + 3 a + 6\bigr] \)