Elliptic curve isogeny class 20.2-b over number field 4.4.11324.1

• Base field: 4.4.11324.1
• Label: 4.4.11324.1-20.2-b
• Conductor: 20.2
• Rank: \( 1 \)

Base field 4.4.11324.1

Generator \(a\), with minimal polynomial \( x^{4} - x^{3} - 5 x^{2} + 4 x + 2 \); class number \(1\).

Elliptic curves in class 20.2-b over 4.4.11324.1

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

Curve label	Weierstrass Coefficients
20.2-b1	\( \bigl[a^{3} + a^{2} - 3 a - 3\) , \( a^{3} - 3 a + 1\) , \( a + 1\) , \( -2 a^{3} + 3 a^{2} + 20 a + 10\) , \( -11 a^{3} + 4 a^{2} + 68 a + 24\bigr] \)
20.2-b2	\( \bigl[a^{3} - 3 a + 1\) , \( a^{3} - a^{2} - 3 a + 4\) , \( 0\) , \( 10 a^{3} - 11 a^{2} - 10 a + 10\) , \( -49 a^{3} + 175 a^{2} - 96 a - 51\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph