Elliptic curve isogeny class 49.1-a over number field 4.4.2624.1

• Base field: 4.4.2624.1
• Label: 4.4.2624.1-49.1-a
• Conductor: 49.1
• Rank: \( 1 \)

Base field 4.4.2624.1

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

Elliptic curves in class 49.1-a over 4.4.2624.1

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

Curve label	Weierstrass Coefficients
49.1-a1	\( \bigl[a^{2} - a - 1\) , \( a^{3} - 2 a^{2} - 2 a\) , \( a + 1\) , \( -2 a^{2} + 5 a\) , \( -2 a^{3} + 7 a^{2} - 4 a - 1\bigr] \)
49.1-a2	\( \bigl[a^{2} - a - 1\) , \( a^{3} - 3 a^{2} - a + 2\) , \( a^{3} - 2 a^{2} - a + 1\) , \( a^{3} - 2 a^{2} - 2 a + 1\) , \( -a^{3} + 4 a^{2} - a - 1\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph