Elliptic curve isogeny class 49.2-a over number field 4.4.4400.1

• Base field: 4.4.4400.1
• Label: 4.4.4400.1-49.2-a
• Conductor: 49.2
• Rank: \( 0 \)

Base field 4.4.4400.1

Generator \(a\), with minimal polynomial \( x^{4} - 7 x^{2} + 11 \); class number \(1\).

Elliptic curves in class 49.2-a over 4.4.4400.1

Isogeny class 49.2-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
49.2-a1	\( \bigl[a + 1\) , \( a^{2} - 3\) , \( a^{3} + a^{2} - 3 a - 3\) , \( -a^{3} + 3 a + 1\) , \( -a^{3} + a^{2} + 2 a - 3\bigr] \)
49.2-a2	\( \bigl[a + 1\) , \( a^{2} - 3\) , \( a^{3} + a^{2} - 3 a - 3\) , \( 4 a^{3} - 5 a^{2} - 12 a + 6\) , \( -a^{3} + 11 a^{2} - 4 a - 37\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph