Elliptic curve isogeny class 33.1-a over number field \(\Q(\sqrt{3}) \)

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-33.1-a
• Conductor: 33.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 33.1-a over \(\Q(\sqrt{3}) \)

Isogeny class 33.1-a contains 4 curves linked by isogenies of degrees dividing 10.

Curve label	Weierstrass Coefficients
33.1-a1	\( \bigl[a + 1\) , \( a + 1\) , \( a\) , \( 22986 a - 39809\) , \( -2497992 a + 4326651\bigr] \)
33.1-a2	\( \bigl[a + 1\) , \( 1\) , \( 1\) , \( 6 a - 8\) , \( 12 a - 19\bigr] \)
33.1-a3	\( \bigl[a + 1\) , \( -a + 1\) , \( a\) , \( 15 a - 28\) , \( 96 a - 167\bigr] \)
33.1-a4	\( \bigl[a + 1\) , \( 1\) , \( 1\) , \( 57891 a - 100269\) , \( -25338895 a + 43888254\bigr] \)

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