Elliptic curve isogeny class 45.1-f over number field 6.6.1241125.1

• Base field: 6.6.1241125.1
• Label: 6.6.1241125.1-45.1-f
• Conductor: 45.1
• Rank: \( 0 \)

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-f over 6.6.1241125.1

Isogeny class 45.1-f contains only one elliptic curve.

Curve label	Weierstrass Coefficients
45.1-f1	\( \bigl[-a^{5} + a^{4} + 6 a^{3} - 3 a^{2} - 8 a - 3\) , \( -2 a^{5} + 15 a^{3} + 3 a^{2} - 26 a - 9\) , \( -a^{5} + 7 a^{3} + 2 a^{2} - 10 a - 6\) , \( -8 a^{5} + 16 a^{4} + 55 a^{3} - 63 a^{2} - 100 a - 27\) , \( -40 a^{5} + 107 a^{4} + 230 a^{3} - 457 a^{2} - 316 a - 32\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph