Elliptic curve isogeny class 4.2-a over number field 3.3.1101.1

• Base field: 3.3.1101.1
• Label: 3.3.1101.1-4.2-a
• Conductor: 4.2
• Rank: \( 0 \)

Base field 3.3.1101.1

Generator \(a\), with minimal polynomial \( x^{3} - x^{2} - 9 x + 12 \); class number \(1\).

Elliptic curves in class 4.2-a over 3.3.1101.1

Isogeny class 4.2-a contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
4.2-a1	\( \bigl[a^{2} + 2 a - 6\) , \( a^{2} + a - 7\) , \( a^{2} + 2 a - 6\) , \( 188 a^{2} + 89 a - 1554\) , \( -2456 a^{2} - 1044 a + 20635\bigr] \)
4.2-a2	\( \bigl[a\) , \( a - 1\) , \( a\) , \( -4885896171 a^{2} - 8244459484 a + 21816908547\) , \( -359131445660112 a^{2} - 605998244007084 a + 1603623595585837\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph