Elliptic curve isogeny class 23.1-a over number field 4.4.11661.1

• Base field: 4.4.11661.1
• Label: 4.4.11661.1-23.1-a
• Conductor: 23.1
• Rank: \( 2 \)

Base field 4.4.11661.1

Generator \(a\), with minimal polynomial \( x^{4} - 2 x^{3} - 4 x^{2} + 5 x + 3 \); class number \(1\).

Elliptic curves in class 23.1-a over 4.4.11661.1

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

Curve label	Weierstrass Coefficients
23.1-a1	\( \bigl[a^{3} - 4 a - 1\) , \( -a^{3} + a^{2} + 3 a\) , \( a + 1\) , \( -3 a^{3} + 9 a + 4\) , \( 5 a^{3} - 2 a^{2} - 23 a - 10\bigr] \)
23.1-a2	\( \bigl[a^{3} - a^{2} - 3 a + 2\) , \( 0\) , \( a + 1\) , \( 41 a^{3} - 144 a^{2} + 64 a + 89\) , \( -356 a^{3} + 1287 a^{2} - 652 a - 696\bigr] \)

Rank

Rank: \( 2 \)

Isogeny matrix

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

Isogeny graph