Elliptic curve isogeny class 2.1-a over number field 4.4.16609.1

• Base field: 4.4.16609.1
• Label: 4.4.16609.1-2.1-a
• Conductor: 2.1
• Rank: \( 0 \)

Base field 4.4.16609.1

Generator \(a\), with minimal polynomial \( x^{4} - 7 x^{2} - x + 9 \); class number \(1\).

Elliptic curves in class 2.1-a over 4.4.16609.1

Isogeny class 2.1-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
2.1-a1	\( \bigl[a^{2} - 4\) , \( a + 1\) , \( a^{3} - 4 a\) , \( 3 a^{3} - 14 a - 7\) , \( 6 a^{3} + 10 a^{2} - 37 a - 57\bigr] \)
2.1-a2	\( \bigl[a\) , \( a^{3} - 2 a^{2} - 4 a + 8\) , \( a + 1\) , \( 2 a^{3} - 3 a^{2} - 10 a + 11\) , \( 2 a^{3} - 8 a + 2\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph