Elliptic curve isogeny class 49.1-a over number field 5.5.38569.1

• Base field: 5.5.38569.1
• Label: 5.5.38569.1-49.1-a
• 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-a over 5.5.38569.1

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

Curve label	Weierstrass Coefficients
49.1-a1	\( \bigl[2 a^{4} + a^{3} - 9 a^{2} - 4 a + 5\) , \( a^{4} - 4 a^{2} + 2\) , \( a^{3} - 3 a + 1\) , \( 15 a^{4} - 4 a^{3} - 65 a^{2} + 4 a + 7\) , \( -24 a^{4} + 3 a^{3} + 20 a^{2} - 133 a + 36\bigr] \)
49.1-a2	\( \bigl[2 a^{4} + a^{3} - 9 a^{2} - 4 a + 5\) , \( a^{4} - 4 a^{2} + 2\) , \( a^{3} - 3 a + 1\) , \( -4 a^{3} - 10 a^{2} - a + 7\) , \( -11 a^{4} - 23 a^{3} + 5 a^{2} + 15 a - 1\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph