Elliptic curve isogeny class 12.1-b over number field 4.4.8112.1

• Base field: 4.4.8112.1
• Label: 4.4.8112.1-12.1-b
• Conductor: 12.1
• Rank: \( 0 \)

Base field 4.4.8112.1

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

Elliptic curves in class 12.1-b over 4.4.8112.1

Isogeny class 12.1-b contains 3 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
12.1-b1	\( \bigl[a^{2} - 2\) , \( -a^{3} + a^{2} + 4 a - 2\) , \( a + 1\) , \( -34 a^{3} + 29 a^{2} + 144 a - 127\) , \( -313 a^{3} - 1350 a^{2} - 646 a + 1667\bigr] \)
12.1-b2	\( \bigl[a^{2} - 2\) , \( -a^{3} + a^{2} + 4 a - 2\) , \( a + 1\) , \( a^{3} - a^{2} - 6 a + 8\) , \( 20 a^{3} + 43 a^{2} - 13 a - 31\bigr] \)
12.1-b3	\( \bigl[a^{2} + a - 2\) , \( a + 1\) , \( a^{2} + a - 3\) , \( 7 a^{3} + 8 a^{2} - 27 a - 28\) , \( 25 a^{3} + 23 a^{2} - 104 a - 92\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph