Elliptic curve isogeny class 49.1-a over number field 5.5.70601.1

• Base field: 5.5.70601.1
• Label: 5.5.70601.1-49.1-a
• 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-a over 5.5.70601.1

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

Curve label	Weierstrass Coefficients
49.1-a1	\( \bigl[3 a^{4} - 2 a^{3} - 15 a^{2} + 2 a + 5\) , \( -a^{3} + a^{2} + 4 a - 2\) , \( a^{4} - a^{3} - 4 a^{2} + a + 1\) , \( -17 a^{4} + 92 a^{2} + 46 a - 22\) , \( 6 a^{4} - 2 a^{3} - 30 a^{2} - 11 a + 8\bigr] \)
49.1-a2	\( \bigl[3 a^{4} - 2 a^{3} - 15 a^{2} + a + 5\) , \( -3 a^{4} + 2 a^{3} + 15 a^{2} - 6\) , \( 3 a^{4} - 2 a^{3} - 15 a^{2} + a + 5\) , \( -2 a^{4} + a^{3} + 8 a^{2} + 3 a + 3\) , \( -11 a^{4} + 7 a^{3} + 56 a^{2} + a - 26\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph