Elliptic curve isogeny class 19.1-b over number field 4.4.5744.1

• Base field: 4.4.5744.1
• Label: 4.4.5744.1-19.1-b
• Conductor: 19.1
• Rank: \( 1 \)

Base field 4.4.5744.1

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

Elliptic curves in class 19.1-b over 4.4.5744.1

Isogeny class 19.1-b contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
19.1-b1	\( \bigl[a^{2} - a - 1\) , \( -a^{3} + 5 a\) , \( a^{2} - 1\) , \( -2 a^{3} - 9 a^{2} - 6 a + 3\) , \( -10 a^{3} - 24 a^{2} - 6 a + 4\bigr] \)
19.1-b2	\( \bigl[-a^{3} + a^{2} + 5 a\) , \( -a^{3} + a^{2} + 5 a - 1\) , \( a^{2} - 2\) , \( 2 a^{3} + a^{2} - 7 a - 6\) , \( -a^{3} + 8 a + 5\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph