Elliptic curve isogeny class 33.1-h over number field 4.4.4752.1

• Base field: 4.4.4752.1
• Label: 4.4.4752.1-33.1-h
• Conductor: 33.1
• Rank: \( 0 \)

Base field 4.4.4752.1

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

Elliptic curves in class 33.1-h over 4.4.4752.1

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

Curve label	Weierstrass Coefficients
33.1-h1	\( \bigl[a^{3} - a^{2} - 3 a + 1\) , \( -a^{3} + 3 a + 2\) , \( 0\) , \( 4 a^{3} - 4 a^{2} - 20 a - 4\) , \( 33 a^{3} - 19 a^{2} - 121 a - 25\bigr] \)
33.1-h2	\( \bigl[a^{3} - a^{2} - 3 a + 1\) , \( -a^{3} + 3 a + 2\) , \( 0\) , \( -a^{3} + a^{2} + 5 a + 1\) , \( 0\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph