Elliptic curve isogeny class 21.1-h over number field 5.5.157457.1

• Base field: 5.5.157457.1
• Label: 5.5.157457.1-21.1-h
• Conductor: 21.1
• Rank: \( 1 \)

Base field 5.5.157457.1

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

Elliptic curves in class 21.1-h over 5.5.157457.1

Isogeny class 21.1-h contains only one elliptic curve.

Curve label	Weierstrass Coefficients
21.1-h1	\( \bigl[a + 1\) , \( -a^{3} + a^{2} + 3 a + 1\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 4 a + 2\) , \( -2 a^{3} + 4 a^{2} + 8 a - 2\) , \( -2 a^{3} + 3 a^{2} + 7 a - 3\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph