Elliptic curve isogeny class 20.2-b over number field 4.4.18625.1

• Base field: 4.4.18625.1
• Label: 4.4.18625.1-20.2-b
• Conductor: 20.2
• Rank: \( 1 \)

Base field 4.4.18625.1

Generator \(a\), with minimal polynomial \( x^{4} - x^{3} - 14 x^{2} + 9 x + 41 \); class number \(1\).

Elliptic curves in class 20.2-b over 4.4.18625.1

Isogeny class 20.2-b contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
20.2-b1	\( \bigl[a^{2} - 6\) , \( a + 1\) , \( \frac{1}{6} a^{3} + a^{2} - \frac{4}{3} a - \frac{35}{6}\) , \( \frac{215}{6} a^{3} + 72 a^{2} - \frac{833}{3} a - \frac{2965}{6}\) , \( -300 a^{3} - 744 a^{2} + 1677 a + 3441\bigr] \)
20.2-b2	\( \bigl[a\) , \( a^{2} + a - 6\) , \( \frac{1}{6} a^{3} + a^{2} - \frac{4}{3} a - \frac{41}{6}\) , \( -a^{3} - 33 a^{2} + 33 a + 142\) , \( -\frac{455}{6} a^{3} - 10 a^{2} + \frac{1106}{3} a + \frac{1759}{6}\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph