Elliptic curve isogeny class 33.2-d over number field \(\Q(\sqrt{3}) \)

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-33.2-d
• Conductor: 33.2
• Rank: \( 0 \)

Base field \(\Q(\sqrt{3}) \)

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

Elliptic curves in class 33.2-d over \(\Q(\sqrt{3}) \)

Isogeny class 33.2-d contains 4 curves linked by isogenies of degrees dividing 10.

Curve label	Weierstrass Coefficients
33.2-d1	\( \bigl[a + 1\) , \( a\) , \( a\) , \( 5 a - 7\) , \( a - 1\bigr] \)
33.2-d2	\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( 460939 a - 798370\) , \( 224206774 a - 388337524\bigr] \)
33.2-d3	\( \bigl[a + 1\) , \( -a\) , \( a\) , \( 8272 a - 14332\) , \( 544260 a - 942688\bigr] \)
33.2-d4	\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( -6 a - 9\) , \( 6 a + 10\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 5 & 10 & 2 \\ 5 & 1 & 2 & 10 \\ 10 & 2 & 1 & 5 \\ 2 & 10 & 5 & 1 \end{array}\right)\)

Isogeny graph