Elliptic curve isogeny class 45.1-g over number field 6.6.1241125.1

• Base field: 6.6.1241125.1
• Label: 6.6.1241125.1-45.1-g
• Conductor: 45.1
• Rank: \( 1 \)

Base field 6.6.1241125.1

Generator \(a\), with minimal polynomial \( x^{6} - 7 x^{4} - 2 x^{3} + 11 x^{2} + 7 x + 1 \); class number \(1\).

Elliptic curves in class 45.1-g over 6.6.1241125.1

Isogeny class 45.1-g contains only one elliptic curve.

Curve label	Weierstrass Coefficients
45.1-g1	\( \bigl[-2 a^{5} + a^{4} + 14 a^{3} - a^{2} - 23 a - 9\) , \( 4 a^{5} - 2 a^{4} - 27 a^{3} + 4 a^{2} + 41 a + 13\) , \( -3 a^{5} + a^{4} + 20 a^{3} - 29 a - 12\) , \( 3 a^{5} + a^{4} - 24 a^{3} - 11 a^{2} + 45 a + 23\) , \( 6 a^{5} - 4 a^{4} - 45 a^{3} + 9 a^{2} + 84 a + 32\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph