Elliptic curve isogeny class 12.1-b over number field 4.4.14272.1

• Base field: 4.4.14272.1
• Label: 4.4.14272.1-12.1-b
• Conductor: 12.1
• Rank: \( 0 \)

Base field 4.4.14272.1

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

Elliptic curves in class 12.1-b over 4.4.14272.1

Isogeny class 12.1-b contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
12.1-b1	\( \bigl[a^{3} - 3 a^{2} - a + 3\) , \( a^{3} - 3 a^{2} - 3 a + 2\) , \( a^{3} - 3 a^{2} - 2 a + 4\) , \( -11 a^{3} - 26 a^{2} + 15 a + 14\) , \( -89 a^{3} - 165 a^{2} + 65 a + 96\bigr] \)
12.1-b2	\( \bigl[2 a^{3} - 5 a^{2} - 6 a + 5\) , \( -a^{3} + 3 a^{2} + 3 a - 2\) , \( 2 a^{3} - 5 a^{2} - 6 a + 4\) , \( -a^{3} + 3 a^{2} + 6 a - 7\) , \( 4 a^{3} - 12 a^{2} - 4 a + 8\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph