Elliptic curve isogeny class 33.1-b over number field 4.4.18736.1

• Base field: 4.4.18736.1
• Label: 4.4.18736.1-33.1-b
• Conductor: 33.1
• Rank: \( 0 \)

Base field 4.4.18736.1

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

Elliptic curves in class 33.1-b over 4.4.18736.1

Isogeny class 33.1-b contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
33.1-b1	\( \bigl[a^{3} - a^{2} - 4 a - 1\) , \( a^{3} - 2 a^{2} - 3 a + 2\) , \( a^{2} - 2\) , \( -21 a^{3} + 43 a^{2} + 131 a - 193\) , \( 342 a^{3} - 1041 a^{2} - 571 a + 1785\bigr] \)
33.1-b2	\( \bigl[a^{3} - a^{2} - 4 a - 1\) , \( a^{3} - 2 a^{2} - 3 a + 2\) , \( a^{2} - 2\) , \( -a^{3} + 3 a^{2} + 6 a - 3\) , \( -2 a^{3} + 8 a^{2} + 8 a - 15\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph