Elliptic curve isogeny class 49.1-a over number field 4.4.4205.1

• Base field: 4.4.4205.1
• Label: 4.4.4205.1-49.1-a
• Conductor: 49.1
• Rank: \( 1 \)

Base field 4.4.4205.1

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

Elliptic curves in class 49.1-a over 4.4.4205.1

Isogeny class 49.1-a contains 4 curves linked by isogenies of degrees dividing 10.

Curve label	Weierstrass Coefficients
49.1-a1	\( \bigl[a^{3} - a^{2} - 4 a\) , \( -a\) , \( 0\) , \( 4 a^{3} - 4 a^{2} - 24 a - 12\) , \( a^{3} - a^{2} - 6 a - 2\bigr] \)
49.1-a2	\( \bigl[a^{3} - a^{2} - 4 a\) , \( -a\) , \( 0\) , \( -a^{3} + a^{2} + 6 a + 3\) , \( 0\bigr] \)
49.1-a3	\( \bigl[1\) , \( -a^{3} + a^{2} + 6 a + 2\) , \( 1\) , \( -2 a^{3} + 2 a^{2} + 12 a - 26\) , \( -16 a^{3} + 16 a^{2} + 96 a - 17\bigr] \)
49.1-a4	\( \bigl[1\) , \( -a^{3} + a^{2} + 6 a + 2\) , \( 1\) , \( -7 a^{3} + 7 a^{2} + 42 a - 11\) , \( -12 a^{3} + 12 a^{2} + 72 a - 25\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)\)

Isogeny graph