Elliptic curve isogeny class 12.2-c over number field 4.4.13768.1

• Base field: 4.4.13768.1
• Label: 4.4.13768.1-12.2-c
• Conductor: 12.2
• Rank: \( 1 \)

Base field 4.4.13768.1

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

Elliptic curves in class 12.2-c over 4.4.13768.1

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

Curve label	Weierstrass Coefficients
12.2-c1	\( \bigl[a^{2} - a - 2\) , \( -a + 1\) , \( a + 1\) , \( 2 a^{3} - 4 a^{2} - 4 a\) , \( 2 a^{3} - a^{2} - 10 a - 4\bigr] \)
12.2-c2	\( \bigl[a\) , \( -a^{3} + a^{2} + 4 a\) , \( a + 1\) , \( 2 a^{3} - a^{2} - 13 a - 5\) , \( 52 a^{3} - 9 a^{2} - 270 a - 124\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph