Elliptic curve isogeny class 44.1-c over number field 4.4.8000.1

• Base field: 4.4.8000.1
• Label: 4.4.8000.1-44.1-c
• 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-c over 4.4.8000.1

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

Curve label	Weierstrass Coefficients
44.1-c1	\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 3 a - 3\) , \( -\frac{1}{2} a^{2} - a + 4\) , \( a + 1\) , \( -\frac{83}{2} a^{3} - \frac{177}{2} a^{2} + 972 a - 1174\) , \( 315 a^{3} + 2922 a^{2} - 17210 a + 19020\bigr] \)
44.1-c2	\( \bigl[\frac{1}{2} a^{3} - 3 a + 1\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 2 a - 2\) , \( \frac{1}{2} a^{2} - 2\) , \( -5 a^{3} - 15 a^{2} + 10 a + 41\) , \( \frac{131}{2} a^{3} + 175 a^{2} - 183 a - 485\bigr] \)