Elliptic curve isogeny class 23.1-b over number field 4.4.4205.1

• Base field: 4.4.4205.1
• Label: 4.4.4205.1-23.1-b
• Conductor: 23.1
• Rank: \( 0 \)

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 23.1-b over 4.4.4205.1

Isogeny class 23.1-b contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
23.1-b1	\( \bigl[0\) , \( 2 a^{3} - 3 a^{2} - 9 a - 1\) , \( a\) , \( a^{3} + 2 a + 5\) , \( -3 a^{2} - 4 a\bigr] \)
23.1-b2	\( \bigl[0\) , \( a^{3} - 2 a^{2} - 3 a\) , \( 1\) , \( -11 a^{3} - 14 a^{2} + a + 2\) , \( -63 a^{3} - 120 a^{2} - 16 a + 23\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph