Elliptic curve isogeny class 45.1-d over number field 5.5.65657.1

• Base field: 5.5.65657.1
• Label: 5.5.65657.1-45.1-d
• Conductor: 45.1
• Rank: \( 0 \)

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 45.1-d over 5.5.65657.1

Isogeny class 45.1-d contains only one elliptic curve.

Curve label	Weierstrass Coefficients
45.1-d1	\( \bigl[-2 a^{4} + 3 a^{3} + 9 a^{2} - 8 a - 7\) , \( -3 a^{4} + 4 a^{3} + 13 a^{2} - 12 a - 9\) , \( a^{4} - a^{3} - 4 a^{2} + 3 a + 3\) , \( -7 a^{4} + 2 a^{3} + 20 a^{2} - 11 a - 2\) , \( -11 a^{4} - 8 a^{3} + 24 a^{2} + 9 a + 2\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph