Elliptic curve isogeny class 44.2-c over number field 4.4.8000.1

• Base field: 4.4.8000.1
• Label: 4.4.8000.1-44.2-c
• Number of curves: 2
• Conductor: 44.2
• 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 44.2-c over 4.4.8000.1

Isogeny class 44.2-c contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
44.2-c1	\( \bigl[\frac{1}{2} a^{2} + a - 2\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + 3 a - 4\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 2 a - 3\) , \( \frac{723}{2} a^{3} + 84 a^{2} - 2089 a - 2043\) , \( -\frac{16043}{2} a^{3} - \frac{6019}{2} a^{2} + 47417 a + 50295\bigr] \)
44.2-c2	\( \bigl[a + 1\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 2 a + 3\) , \( \frac{1}{2} a^{2} + a - 3\) , \( -\frac{21}{2} a^{3} + 18 a^{2} + 76 a - 126\) , \( 121 a^{3} - \frac{407}{2} a^{2} - 877 a + 1465\bigr] \)