Elliptic curve isogeny class 55.2-b over number field 4.4.4400.1

• Base field: 4.4.4400.1
• Label: 4.4.4400.1-55.2-b
• Conductor: 55.2
• Rank: \( 1 \)

Base field 4.4.4400.1

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

Elliptic curves in class 55.2-b over 4.4.4400.1

Isogeny class 55.2-b contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
55.2-b1	\( \bigl[a^{3} + a^{2} - 3 a - 4\) , \( a^{3} - 4 a\) , \( a^{3} + a^{2} - 3 a - 3\) , \( 4 a^{3} + 4 a^{2} - 18 a - 20\) , \( 5 a^{3} + 7 a^{2} - 23 a - 33\bigr] \)
55.2-b2	\( \bigl[a^{2} + a - 3\) , \( a + 1\) , \( a^{2} + a - 4\) , \( -5 a^{3} + 10 a^{2} + 26 a - 43\) , \( -9 a^{3} + 17 a^{2} + 43 a - 73\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph