Elliptic curve isogeny class 33.1-d over number field \(\Q(\sqrt{165}) \)

• Base field: \(\Q(\sqrt{165}) \)
• Label: 2.2.165.1-33.1-d
• Conductor: 33.1
• Rank: \( 2 \)

Base field \(\Q(\sqrt{165}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 41 \); class number \(2\).

Elliptic curves in class 33.1-d over \(\Q(\sqrt{165}) \)

Isogeny class 33.1-d contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
33.1-d1	\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( -5093 a + 35268\) , \( -193596 a + 1340204\bigr] \)
33.1-d2	\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( 1342 a - 9282\) , \( -14406 a + 99734\bigr] \)
33.1-d3	\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( 757 a - 5232\) , \( 32808 a - 227110\bigr] \)
33.1-d4	\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( 17137 a - 118632\) , \( -3003792 a + 20794100\bigr] \)

Rank

Rank: \( 2 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph