Elliptic curve isogeny class 8.1-a over number field 3.3.733.1

• Base field: 3.3.733.1
• Label: 3.3.733.1-8.1-a
• Conductor: 8.1
• 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 8.1-a over 3.3.733.1

Isogeny class 8.1-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
8.1-a1	\( \bigl[a^{2} - 5\) , \( a^{2} + a - 4\) , \( a^{2} + a - 4\) , \( -3 a^{2} - 9 a + 13\) , \( 3 a^{2} + 2 a - 7\bigr] \)
8.1-a2	\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( -3347017855 a^{2} - 5081438155 a + 10633054035\) , \( 197015090442315 a^{2} + 299108054057184 a - 625892120411371\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph