Elliptic curve isogeny class 47.2-b over number field 5.5.70601.1

• Base field: 5.5.70601.1
• Label: 5.5.70601.1-47.2-b
• Conductor: 47.2
• Rank: \( 1 \)

Base field 5.5.70601.1

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

Elliptic curves in class 47.2-b over 5.5.70601.1

Isogeny class 47.2-b contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
47.2-b1	\( \bigl[a^{4} - a^{3} - 5 a^{2} + 3 a + 3\) , \( -2 a^{4} + a^{3} + 11 a^{2} + a - 6\) , \( a + 1\) , \( -2 a^{4} + a^{3} + 11 a^{2} + a - 7\) , \( 0\bigr] \)
47.2-b2	\( \bigl[3 a^{4} - 2 a^{3} - 15 a^{2} + 2 a + 5\) , \( -a^{3} + 2 a^{2} + 4 a - 4\) , \( 2 a^{4} - a^{3} - 10 a^{2} + 3\) , \( 4 a^{4} - 6 a^{3} - 10 a^{2} + 2 a - 3\) , \( 19 a^{4} - 11 a^{3} - 83 a^{2} - 29 a + 17\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph