Elliptic curve isogeny class 19.1-a over number field 4.4.11324.1

• Base field: 4.4.11324.1
• Label: 4.4.11324.1-19.1-a
• Conductor: 19.1
• Rank bounds: 0...1

Base field 4.4.11324.1

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

Elliptic curves in class 19.1-a over 4.4.11324.1

Isogeny class 19.1-a contains only one elliptic curve.

Curve label	Weierstrass Coefficients
19.1-a1	\( \bigl[a^{3} - 4 a\) , \( a^{3} + a^{2} - 3 a - 3\) , \( a^{3} - 4 a + 1\) , \( -69 a^{3} - 86 a^{2} + 149 a + 58\) , \( -989 a^{3} - 1242 a^{2} + 2142 a + 875\bigr] \)

Rank

Rank \(r\) satisfies \(0 \le r \le 1\)

Isogeny matrix

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

Isogeny graph