Elliptic curve isogeny class 20.2-a over number field 4.4.16448.1

• Base field: 4.4.16448.1
• Label: 4.4.16448.1-20.2-a
• Conductor: 20.2
• Rank: \( 1 \)

Base field 4.4.16448.1

Generator \(a\), with minimal polynomial \( x^{4} - 2 x^{3} - 6 x^{2} + 2 \); class number \(1\).

Elliptic curves in class 20.2-a over 4.4.16448.1

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

Curve label	Weierstrass Coefficients
20.2-a1	\( \bigl[0\) , \( -a^{3} + 2 a^{2} + 4 a + 1\) , \( 2 a^{3} - 5 a^{2} - 7 a + 2\) , \( a^{3} - 5 a^{2} + 6 a + 7\) , \( -3 a^{3} + 7 a^{2} + 10 a - 1\bigr] \)
20.2-a2	\( \bigl[2 a^{3} - 5 a^{2} - 8 a + 2\) , \( -a^{3} + 3 a^{2} + 4 a - 3\) , \( 0\) , \( a^{3} + 11 a^{2} + 8 a - 5\) , \( 9 a^{3} + 12 a^{2} - 4 a - 2\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph