Elliptic curve isogeny class 19.1-a over number field 5.5.65657.1

• Base field: 5.5.65657.1
• Label: 5.5.65657.1-19.1-a
• Conductor: 19.1
• Rank: \( 1 \)

Base field 5.5.65657.1

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

Elliptic curves in class 19.1-a over 5.5.65657.1

Isogeny class 19.1-a contains only one elliptic curve.

Curve label	Weierstrass Coefficients
19.1-a1	\( \bigl[a^{4} - a^{3} - 4 a^{2} + 2 a + 2\) , \( a^{4} - a^{3} - 5 a^{2} + 4 a + 4\) , \( -a^{4} + a^{3} + 5 a^{2} - 3 a - 4\) , \( 4 a^{4} - 5 a^{3} - 17 a^{2} + 12 a + 16\) , \( 2 a^{4} - 2 a^{3} - 10 a^{2} + 6 a + 9\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph