Elliptic curve isogeny class 3364.1-d over number field \(\Q(\sqrt{3}) \)

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-3364.1-d
• Conductor: 3364.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 3364.1-d over \(\Q(\sqrt{3}) \)

Isogeny class 3364.1-d contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
3364.1-d1	\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -5 a - 9\) , \( 7 a + 12\bigr] \)
3364.1-d2	\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 35 a + 61\) , \( -143 a - 248\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph