Elliptic curve isogeny class 44.4-b over number field 4.4.8000.1

• Base field: 4.4.8000.1
• Label: 4.4.8000.1-44.4-b
• Conductor: 44.4
• Rank bounds: 0...1

Base field 4.4.8000.1

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

Rank

Rank \(r\) satisfies \(0 \le r \le 1\)

Isogeny matrix

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

Isogeny graph

Elliptic curves in class 44.4-b over 4.4.8000.1

Isogeny class 44.4-b contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
44.4-b1	\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 3 a - 2\) , \( -\frac{1}{2} a^{2} + a + 3\) , \( \frac{1}{2} a^{2} + a - 3\) , \( -19 a^{3} - \frac{49}{2} a^{2} + 181 a - 143\) , \( 1176 a^{3} - \frac{4693}{2} a^{2} - 8209 a + 14708\bigr] \)
44.4-b2	\( \bigl[\frac{1}{2} a^{2} - 2\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 4 a + 3\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 2 a - 2\) , \( \frac{5}{2} a^{3} + \frac{3}{2} a^{2} - 19 a - 12\) , \( \frac{81}{2} a^{3} + \frac{129}{2} a^{2} - 294 a - 473\bigr] \)