Elliptic curve isogeny class 23.2-b over number field 4.4.4752.1

• Base field: 4.4.4752.1
• Label: 4.4.4752.1-23.2-b
• Conductor: 23.2
• Rank: \( 1 \)

Base field 4.4.4752.1

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

Elliptic curves in class 23.2-b over 4.4.4752.1

Isogeny class 23.2-b contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
23.2-b1	\( \bigl[a^{2} - a - 1\) , \( a^{3} - a^{2} - 3 a + 2\) , \( a^{3} - 4 a\) , \( -4 a^{3} - 4 a^{2} + 7 a + 4\) , \( 23 a^{3} + 10 a^{2} - 41 a - 9\bigr] \)
23.2-b2	\( \bigl[a^{3} - a^{2} - 3 a + 2\) , \( a^{3} - 2 a^{2} - 3 a + 4\) , \( a^{2} - a - 2\) , \( 4 a^{3} - 9 a^{2} - 8 a + 14\) , \( 2 a^{3} - 5 a^{2} - 3 a + 8\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph