Elliptic curve isogeny class 225.1-k over number field 5.5.65657.1

• Base field: 5.5.65657.1
• Label: 5.5.65657.1-225.1-k
• Conductor: 225.1
• 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 225.1-k over 5.5.65657.1

Isogeny class 225.1-k contains only one elliptic curve.

Curve label	Weierstrass Coefficients
225.1-k1	\( \bigl[-2 a^{4} + 3 a^{3} + 9 a^{2} - 8 a - 7\) , \( a^{3} - 4 a - 1\) , \( a^{4} - a^{3} - 4 a^{2} + 3 a + 2\) , \( -a^{4} + 3 a^{3} - 8 a + 10\) , \( 951 a^{4} - 1684 a^{3} - 3458 a^{2} + 4566 a + 1238\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph