Elliptic curve isogeny class 49.1-b over number field 5.5.38569.1

• Base field: 5.5.38569.1
• Label: 5.5.38569.1-49.1-b
• Conductor: 49.1
• Rank: \( 0 \)

Base field 5.5.38569.1

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

Elliptic curves in class 49.1-b over 5.5.38569.1

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

Curve label	Weierstrass Coefficients
49.1-b1	\( \bigl[a^{2} + a - 2\) , \( 2 a^{4} + a^{3} - 9 a^{2} - 5 a + 3\) , \( 2 a^{4} + a^{3} - 9 a^{2} - 4 a + 4\) , \( 20 a^{4} + 19 a^{3} - 96 a^{2} - 67 a + 27\) , \( -119 a^{4} - 76 a^{3} + 494 a^{2} + 383 a - 143\bigr] \)
49.1-b2	\( \bigl[a^{2} + a - 2\) , \( 2 a^{4} + a^{3} - 9 a^{2} - 5 a + 3\) , \( 2 a^{4} + a^{3} - 9 a^{2} - 4 a + 4\) , \( -a^{3} - a^{2} + 3 a + 2\) , \( -2 a^{4} - a^{3} + 7 a^{2} + 5 a - 3\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph