Elliptic curve isogeny class 12.2-d over number field 4.4.17428.1

• Base field: 4.4.17428.1
• Label: 4.4.17428.1-12.2-d
• Conductor: 12.2
• Rank: \( 0 \)

Base field 4.4.17428.1

Generator \(a\), with minimal polynomial \( x^{4} - x^{3} - 6 x^{2} + 4 x + 6 \); class number \(1\).

Elliptic curves in class 12.2-d over 4.4.17428.1

Isogeny class 12.2-d contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
12.2-d1	\( \bigl[a^{3} + a^{2} - 4 a - 3\) , \( a^{3} - 4 a - 2\) , \( a^{2} + a - 2\) , \( 3 a^{3} + 2 a^{2} - 6 a - 7\) , \( 11 a^{3} - 3 a^{2} - 41 a + 25\bigr] \)
12.2-d2	\( \bigl[a^{2} + a - 3\) , \( a^{3} - 4 a - 2\) , \( a^{2} + a - 2\) , \( -31 a^{3} - 38 a^{2} + 86 a + 73\) , \( -559 a^{3} - 771 a^{2} + 1545 a + 1421\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph