Elliptic curve isogeny class 19.1-e over number field 4.4.8069.1

• Base field: 4.4.8069.1
• Label: 4.4.8069.1-19.1-e
• Conductor: 19.1
• Rank: \( 0 \)

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 19.1-e over 4.4.8069.1

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

Curve label	Weierstrass Coefficients
19.1-e1	\( \bigl[a^{2} - 3\) , \( -a^{3} + 5 a - 1\) , \( a^{3} + a^{2} - 3 a - 1\) , \( -16 a^{3} + 12 a^{2} + 72 a - 84\) , \( 11 a^{3} - 32 a^{2} - 66 a + 111\bigr] \)
19.1-e2	\( \bigl[a^{2} - 3\) , \( -a^{3} + 5 a - 1\) , \( a^{3} + a^{2} - 3 a - 1\) , \( -a^{3} - 8 a^{2} - 3 a + 21\) , \( -5 a^{3} - 12 a^{2} + 7 a + 20\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph