Elliptic curve isogeny class 44.3-b over number field 4.4.8000.1

• Base field: 4.4.8000.1
• Label: 4.4.8000.1-44.3-b
• Conductor: 44.3
• 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 44.3-b over 4.4.8000.1

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

Curve label	Weierstrass Coefficients
44.3-b1	\( \bigl[\frac{1}{2} a^{2} - 3\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + 2 a - 2\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 2 a - 3\) , \( -\frac{3}{2} a^{3} - \frac{3}{2} a^{2} + 3 a + 3\) , \( -25 a^{3} - \frac{133}{2} a^{2} + 68 a + 182\bigr] \)
44.3-b2	\( \bigl[\frac{1}{2} a^{2} + a - 3\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 3 a - 2\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 3 a - 2\) , \( 34 a^{3} + \frac{45}{2} a^{2} - 167 a - 378\) , \( -\frac{1153}{2} a^{3} + \frac{4693}{2} a^{2} + 1106 a - 8757\bigr] \)