Elliptic curve isogeny class 41.1-b over number field 4.4.2624.1

• Base field: 4.4.2624.1
• Label: 4.4.2624.1-41.1-b
• Conductor: 41.1
• Rank: \( 0 \)

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 41.1-b over 4.4.2624.1

Isogeny class 41.1-b contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
41.1-b1	\( \bigl[a^{3} - a^{2} - 3 a\) , \( -a^{3} + 3 a^{2} - a - 2\) , \( a^{3} - 2 a^{2} - a + 1\) , \( -6 a^{3} + 16 a^{2} + 6 a - 17\) , \( -a^{3} + 2 a^{2} + a + 1\bigr] \)
41.1-b2	\( \bigl[a^{3} - 2 a^{2} - 2 a + 1\) , \( a^{3} - 2 a^{2} - 3 a + 1\) , \( a^{3} - 2 a^{2} - a + 2\) , \( 5 a^{3} - 13 a^{2} - 10 a + 15\) , \( 2 a^{3} - 6 a^{2} - 4 a + 7\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph