Elliptic curve isogeny class 512.4-i over number field \(\Q(\sqrt{33}) \)

• Base field: \(\Q(\sqrt{33}) \)
• Label: 2.2.33.1-512.4-i
• Conductor: 512.4
• Rank: \( 1 \)

Base field \(\Q(\sqrt{33}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 8 \); class number \(1\).

Elliptic curves in class 512.4-i over \(\Q(\sqrt{33}) \)

Isogeny class 512.4-i contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
512.4-i1	\( \bigl[0\) , \( -a\) , \( 0\) , \( 170 a + 405\) , \( 171 a + 406\bigr] \)
512.4-i2	\( \bigl[0\) , \( -a\) , \( 0\) , \( 2 a - 3\) , \( 4963 a - 16738\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph