Elliptic curve isogeny class 33.1-c over number field 4.4.4752.1

• Base field: 4.4.4752.1
• Label: 4.4.4752.1-33.1-c
• 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-c over 4.4.4752.1

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

Curve label	Weierstrass Coefficients
33.1-c1	\( \bigl[a^{3} - a^{2} - 3 a + 1\) , \( -a^{3} + 3 a\) , \( a^{3} - 4 a\) , \( -5 a^{3} + 11 a^{2} + 20 a - 33\) , \( 18 a^{3} - 47 a^{2} - 36 a + 78\bigr] \)
33.1-c2	\( \bigl[a^{3} - a^{2} - 3 a + 1\) , \( -a^{3} + 3 a\) , \( a^{3} - 4 a\) , \( a^{2} - 3\) , \( -2 a^{2} - a + 1\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph