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

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-3249.1-a
• 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-a over \(\Q(\sqrt{3}) \)

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

Curve label	Weierstrass Coefficients
3249.1-a1	\( \bigl[a\) , \( a\) , \( 0\) , \( 61 a - 105\) , \( -350 a + 605\bigr] \)
3249.1-a2	\( \bigl[a\) , \( a\) , \( 0\) , \( -29 a + 30\) , \( -1178 a + 1982\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph