Elliptic curve isogeny class 49.3-a over number field 4.4.4205.1

• Base field: 4.4.4205.1
• Label: 4.4.4205.1-49.3-a
• Conductor: 49.3
• 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 49.3-a over 4.4.4205.1

Isogeny class 49.3-a contains 2 curves linked by isogenies of degree 7.

Curve label	Weierstrass Coefficients
49.3-a1	\( \bigl[a^{3} - a^{2} - 4 a - 1\) , \( -a^{3} + 2 a^{2} + 2 a\) , \( -a^{3} + 2 a^{2} + 4 a - 1\) , \( -a^{3} + 3 a^{2} - 2 a\) , \( -2 a^{3} + 4 a^{2} + 4 a - 1\bigr] \)
49.3-a2	\( \bigl[a^{3} - a^{2} - 5 a\) , \( -a^{3} + a^{2} + 6 a\) , \( a^{3} - a^{2} - 5 a\) , \( -27 a^{3} - 47 a^{2} - 2 a + 5\) , \( -339 a^{3} - 626 a^{2} - 83 a + 114\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph