Elliptic curve isogeny class 43.1-b over number field 6.6.1683101.1

• Base field: 6.6.1683101.1
• Label: 6.6.1683101.1-43.1-b
• Conductor: 43.1
• Rank: \( 1 \)

Base field 6.6.1683101.1

Generator \(a\), with minimal polynomial \( x^{6} - 3 x^{5} - 4 x^{4} + 13 x^{3} + 7 x^{2} - 14 x - 7 \); class number \(1\).

Elliptic curves in class 43.1-b over 6.6.1683101.1

Isogeny class 43.1-b contains only one elliptic curve.

Curve label	Weierstrass Coefficients
43.1-b1	\( \bigl[a^{5} - 2 a^{4} - 4 a^{3} + 5 a^{2} + 6 a + 1\) , \( a^{5} - 2 a^{4} - 4 a^{3} + 4 a^{2} + 7 a + 3\) , \( a^{5} - 2 a^{4} - 3 a^{3} + 5 a^{2} + 2 a - 1\) , \( -4 a^{5} + 22 a^{4} - 11 a^{3} - 98 a^{2} + 64 a + 138\) , \( -42 a^{5} + 155 a^{4} + 69 a^{3} - 639 a^{2} + 90 a + 692\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph