Elliptic curve isogeny class 25.1-e over number field 6.6.1541581.1

• Base field: 6.6.1541581.1
• Label: 6.6.1541581.1-25.1-e
• Conductor: 25.1
• Rank: \( 1 \)

Base field 6.6.1541581.1

Generator \(a\), with minimal polynomial \( x^{6} - x^{5} - 6 x^{4} + 2 x^{3} + 9 x^{2} + x - 1 \); class number \(1\).

Elliptic curves in class 25.1-e over 6.6.1541581.1

Isogeny class 25.1-e contains only one elliptic curve.

Curve label	Weierstrass Coefficients
25.1-e1	\( \bigl[2 a^{5} - 4 a^{4} - 7 a^{3} + 10 a^{2} + 6 a - 2\) , \( a^{5} - 2 a^{4} - 4 a^{3} + 5 a^{2} + 4 a + 1\) , \( 3 a^{5} - 5 a^{4} - 13 a^{3} + 12 a^{2} + 13 a\) , \( -a^{4} + 5 a^{2} + 3 a + 3\) , \( -2 a^{5} + 11 a^{3} + 6 a^{2} - 6 a + 1\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph