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

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-33.1-d
• 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-d over \(\Q(\sqrt{3}) \)

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

Curve label	Weierstrass Coefficients
33.1-d1	\( \bigl[a + 1\) , \( a\) , \( 1\) , \( 22985 a - 39809\) , \( 2481167 a - 4297507\bigr] \)
33.1-d2	\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( 5 a - 9\) , \( -6 a + 10\bigr] \)
33.1-d3	\( \bigl[a + 1\) , \( 0\) , \( a\) , \( 16 a - 29\) , \( -80 a + 138\bigr] \)
33.1-d4	\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( 57890 a - 100270\) , \( 25396786 a - 43988524\bigr] \)

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