Elliptic curve isogeny class 3249.1-d over number field \(\Q(\sqrt{3}) \)

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-3249.1-d
• Conductor: 3249.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 3249.1-d over \(\Q(\sqrt{3}) \)

Isogeny class 3249.1-d contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
3249.1-d1	\( \bigl[1\) , \( -a - 1\) , \( 0\) , \( 61 a - 105\) , \( 350 a - 605\bigr] \)
3249.1-d2	\( \bigl[1\) , \( -a - 1\) , \( 0\) , \( -29 a + 30\) , \( 1178 a - 1982\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph