Elliptic curve isogeny class 49.1-b over number field 5.5.70601.1

• Base field: 5.5.70601.1
• Label: 5.5.70601.1-49.1-b
• Conductor: 49.1
• Rank: \( 0 \)

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 49.1-b over 5.5.70601.1

Isogeny class 49.1-b contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
49.1-b1	\( \bigl[a^{4} - 6 a^{2} - 2 a + 3\) , \( -a^{4} + a^{3} + 4 a^{2} + 1\) , \( 2 a^{4} - a^{3} - 11 a^{2} + 6\) , \( -11 a^{4} + 16 a^{3} + 42 a^{2} - 35 a + 3\) , \( -89 a^{4} + 160 a^{3} + 310 a^{2} - 419 a + 92\bigr] \)
49.1-b2	\( \bigl[3 a^{4} - 2 a^{3} - 15 a^{2} + a + 6\) , \( a^{4} - a^{3} - 4 a^{2} + 2 a - 1\) , \( 2 a^{4} - a^{3} - 11 a^{2} + a + 6\) , \( a^{4} + 2 a^{3} - 8 a^{2} - 9 a - 1\) , \( -12 a^{4} + 4 a^{3} + 59 a^{2} + 22 a - 16\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph