Elliptic curve isogeny class 4.2-a over number field 3.3.733.1

• Base field: 3.3.733.1
• Label: 3.3.733.1-4.2-a
• Conductor: 4.2
• Rank: \( 0 \)

Base field 3.3.733.1

Generator \(a\), with minimal polynomial \( x^{3} - x^{2} - 7 x + 8 \); class number \(1\).

Elliptic curves in class 4.2-a over 3.3.733.1

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

Curve label	Weierstrass Coefficients
4.2-a1	\( \bigl[a^{2} + a - 4\) , \( -a^{2} + a + 5\) , \( a^{2} - 4\) , \( -4 a^{2} - 6 a + 20\) , \( -15 a^{2} - 20 a + 48\bigr] \)
4.2-a2	\( \bigl[a\) , \( a\) , \( 0\) , \( 1117 a^{2} + 1696 a - 3548\) , \( -21789 a^{2} - 33080 a + 69221\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph