Elliptic curve isogeny class 19.1-a over number field 4.4.8789.1

• Base field: 4.4.8789.1
• Label: 4.4.8789.1-19.1-a
• Conductor: 19.1
• Rank: \( 1 \)

Base field 4.4.8789.1

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

Elliptic curves in class 19.1-a over 4.4.8789.1

Isogeny class 19.1-a contains only one elliptic curve.

Curve label	Weierstrass Coefficients
19.1-a1	\( \bigl[a^{3} - a^{2} - 6 a - 1\) , \( -2 a^{3} + 3 a^{2} + 11 a\) , \( 1\) , \( 2 a^{3} - 5 a^{2} - 6 a + 10\) , \( -6 a^{3} + 10 a^{2} + 29 a - 6\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{r} 1 \end{array}\right)\)

Isogeny graph