Elliptic curve isogeny class 19.2-b over number field 4.4.8069.1

• Base field: 4.4.8069.1
• Label: 4.4.8069.1-19.2-b
• Conductor: 19.2
• Rank: \( 1 \)

Base field 4.4.8069.1

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

Elliptic curves in class 19.2-b over 4.4.8069.1

Isogeny class 19.2-b contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
19.2-b1	\( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( a^{3} - a^{2} - 5 a + 3\) , \( a\) , \( 3 a^{3} - 12 a^{2} + 12 a + 8\) , \( -8 a^{3} - 9 a^{2} + 55 a + 12\bigr] \)
19.2-b2	\( \bigl[a^{3} - 3 a + 1\) , \( a^{3} - 4 a\) , \( a^{2} - 3\) , \( -2 a^{3} - a^{2} + 6 a\) , \( -6 a^{3} - 7 a^{2} + 15 a + 2\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph