Elliptic curve isogeny class 8.1-b over number field 3.3.1229.1

• Base field: 3.3.1229.1
• Label: 3.3.1229.1-8.1-b
• Conductor: 8.1
• Rank: \( 0 \)

Base field 3.3.1229.1

Generator \(a\), with minimal polynomial \( x^{3} - x^{2} - 7 x + 6 \); class number \(1\).

Elliptic curves in class 8.1-b over 3.3.1229.1

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

Curve label	Weierstrass Coefficients
8.1-b1	\( \bigl[a^{2} - 5\) , \( a^{2} + a - 5\) , \( a^{2} + a - 4\) , \( -210 a^{2} + 805 a - 617\) , \( -5560 a^{2} + 19866 a - 12565\bigr] \)
8.1-b2	\( \bigl[1\) , \( -a^{2} - a + 4\) , \( 1\) , \( 4 a - 2\) , \( -a^{2} + 3 a - 2\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph