Elliptic curve isogeny class 55.1-a over number field 4.4.5125.1

• Base field: 4.4.5125.1
• Label: 4.4.5125.1-55.1-a
• Conductor: 55.1
• Rank: \( 0 \)

Base field 4.4.5125.1

Generator \(a\), with minimal polynomial \( x^{4} - 2 x^{3} - 6 x^{2} + 7 x + 11 \); class number \(1\).

Elliptic curves in class 55.1-a over 4.4.5125.1

Isogeny class 55.1-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
55.1-a1	\( \bigl[a^{3} - a^{2} - 3 a + 1\) , \( -a^{3} + a^{2} + 3 a - 1\) , \( a + 1\) , \( -66 a^{3} + 194 a^{2} + 198 a - 666\) , \( -655 a^{3} + 2069 a^{2} + 1528 a - 6306\bigr] \)
55.1-a2	\( \bigl[a^{3} - a^{2} - 3 a + 1\) , \( -a^{3} + a^{2} + 3 a - 1\) , \( a + 1\) , \( 4 a^{3} - 16 a^{2} - 7 a + 49\) , \( -45 a^{3} + 141 a^{2} + 111 a - 443\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph